Ambassador Rémi Eismann<p>A031924: Primes followed by a gap of 6, i.e., next prime is p + 6</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A031924.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A031924.</span><span class="invisible">html</span></a><br>3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A031924.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/A0319</span><span class="invisible">24.html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A031924.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A031924.html</span></a></p><p><a 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#decompwlj
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Rémi Eismann<p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> ➡️ It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.</p><p>We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. For natural numbers, the weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1).</p><p>For prime numbers, this decomposition led to a new classification of primes. Primes classified by weight follow Legendre conjecture and i conjecture that primes classified by level rarefy. I think this conjecture is very important for the distribution of primes.</p><p>It's easy to see and prove that lesser of twin primes (>3) have a weight of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a weight of 3.</p><p>I am not mathematician so i decompose sequences to promote my vision of numbers. By doing these decompositions, i apply a kind of sieve on each sequences.</p><p>➡️ <a href="https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Decomposition_in</span><span class="invisible">to_weight_*_level_%2B_jump</span></a></p>
Rémi Eismann<p>A006073: Numbers k such that k, k+1 and k+2 all have the same number of distinct prime divisors</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A006073.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A006073.</span><span class="invisible">html</span></a><br>3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A006073.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/A0060</span><span class="invisible">73.html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A006073.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A006073.html</span></a></p><p><a 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class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" 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rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>research</span></a></p>
Rémi Eismann<p>A004744: Numbers whose binary expansion does not contain 011</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A004744.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A004744.</span><span class="invisible">html</span></a><br>3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A004744.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/A0047</span><span class="invisible">44.html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A004744.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A004744.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a 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target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>research</span></a></p>
Rémi Eismann<p>My first, favorite and most important sequence, the weights of prime numbers: A117078<br>We see prime numbers classified by level and by weight on the graph.<br>➡️ <a href="https://oeis.org/A117078" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">oeis.org/A117078</span><span class="invisible"></span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a></p>
Rémi Eismann<p>Now this animation is available for the 1000 sequences decomposed on my website.<br>Accessible from the 3Dgraph, 2Dgraph500terms and 2dgraphs pages ➡️ <a href="https://decompwlj.com" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="">decompwlj.com</span><span class="invisible"></span></a><br>A little more work on axis sizing and controls.</p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/palindromes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>palindromes</span></a> <a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>animation</span></a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FundamentalTheoremOfArithmetic</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>research</span></a></p>
Rémi Eismann<p>4: The palindromes in base 10 (A002113) ➡️ <a href="https://decompwlj.com/3DgraphGen/Palindromes.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/Palin</span><span class="invisible">dromes.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/palindromes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>palindromes</span></a> <a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>animation</span></a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FundamentalTheoremOfArithmetic</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>research</span></a></p>
Rémi Eismann<p>3: The triangular numbers (A000217) ➡️ <a href="https://decompwlj.com/3DgraphGen/Triangular_numbers.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/Trian</span><span class="invisible">gular_numbers.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/palindromes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>palindromes</span></a> <a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>animation</span></a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FundamentalTheoremOfArithmetic</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>research</span></a></p>
Rémi Eismann<p>2: The prime numbers (A000040) ➡️ <a href="https://decompwlj.com/3DgraphGen/Prime_numbers.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/Prime</span><span class="invisible">_numbers.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/palindromes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>palindromes</span></a> <a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>animation</span></a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FundamentalTheoremOfArithmetic</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/research" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>research</span></a></p>
Rémi Eismann<p>Generation of four sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:<br>🧵⬇️</p><p>1: The natural numbers (A000027) ➡️ <a href="https://decompwlj.com/3DgraphGen/Natural_numbers.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/Natur</span><span class="invisible">al_numbers.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/palindromes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>palindromes</span></a> <a href="https://mathstodon.xyz/tags/animation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>animation</span></a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FundamentalTheoremOfArithmetic</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/number" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>number</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> 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Rémi Eismann<p>One day, one decomposition<br>A000069: Odious numbers: numbers with an odd number of 1's in their binary expansion</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/Odious_numbers.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/Odious_n</span><span class="invisible">umbers.html</span></a><br>3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/Odious_numbers.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/Odiou</span><span class="invisible">s_numbers.html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/Odious_numbers.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">Odious_numbers.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/binary" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>binary</span></a> <a href="https://mathstodon.xyz/tags/expansion" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>expansion</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a></p>
Rémi Eismann<p>One day, one decomposition<br>A274357: Numbers n such that n and n+1 both have 8 divisors</p><p>3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A274357.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3Dgraph/A274357.</span><span class="invisible">html</span></a><br>3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A274357.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/3DgraphGen/A2743</span><span class="invisible">57.html</span></a><br>2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A274357.html" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">decompwlj.com/2Dgraph500terms/</span><span class="invisible">A274357.html</span></a></p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/divisors" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>divisors</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a></p>
Rémi Eismann<p>The triangular numbers (A000217):</p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/triangular" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>triangular</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a></p>
Rémi Eismann<p>The prime numbers (A000040):</p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a></p>
Rémi Eismann<p>Generation of three sequences decomposed into weight × level + jump (log(weight), log(level), log(jump)) - three.js animation:<br>🧵<br>The natural numbers (A000027):</p><p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequence</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>javascript</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a></p>
Rémi Eismann<p><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decompwlj</span></a> ➡️ It's a decomposition of positive integers. The weight is the smallest such that in the Euclidean division of a number by its weight, the remainder is the jump (first difference, gap). The quotient will be the level. So to decompose a(n), we need a(n+1) with a(n+1)>a(n) (strictly increasing sequence), the decomposition is possible if a(n+1)<3/2×a(n) and we have the unique decomposition a(n) = weight × level + jump.</p><p>We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. For natural numbers, the weight is the smallest prime factor of (n-1) and the level is the largest proper divisor of (n-1). Natural numbers classified by level are the (primes + 1) and natural numbers classified by weight are the (composites +1).</p><p>For prime numbers, this decomposition led to a new classification of primes. Primes classified by weight follow Legendre conjecture and i conjecture that primes classified by level rarefy. I think this conjecture is very important for the distribution of primes.</p><p>It's easy to see and prove that lesser of twin primes (>3) have a weight of 3. So the twin primes conjecture can be rewritten: there are infinitely many primes that have a weight of 3.</p><p>I am not mathematician so i decompose sequences to promote my vision of numbers. By doing these decompositions, i apply a kind of sieve on each sequences.</p><p>➡️ <a href="https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">oeis.org/wiki/Decomposition_in</span><span class="invisible">to_weight_*_level_%2B_jump</span></a></p><p><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>math</span></a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>maths</span></a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>mathematics</span></a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sequences</span></a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OEIS</span></a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>NumberTheory</span></a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PrimeNumbers</span></a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>JavaScript</span></a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>php</span></a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graph</span></a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>3D</span></a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>classification</span></a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>primes</span></a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>threejs</span></a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>webGL</span></a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>integer</span></a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>decomposition</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>numbers</span></a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theory</span></a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>equation</span></a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>graphs</span></a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>sieve</span></a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>fundamental</span></a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>theorem</span></a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>arithmetic</span></a></p>
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