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Rémi EismannOne day, one decomposition A274357: Numbers n such that n and n+1 both have 8 divisors3D graph, threejs - webGL ➡️ <a href="https://decompwlj.com/3Dgraph/A274357.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://decompwlj.com/3Dgraph/A274357.html</a> 3D graph Gen, threejs animation ➡️ <a href="https://decompwlj.com/3DgraphGen/A274357.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://decompwlj.com/3DgraphGen/A274357.html</a> 2D graph, first 500 terms ➡️ <a href="https://decompwlj.com/2Dgraph500terms/A274357.html" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://decompwlj.com/2Dgraph500terms/A274357.html</a><a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequence" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sequence</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/javascript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#javascript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/divisors" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#divisors</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#webGL</a>

Rémi EismannA short story about my decomposition into weight × level + jump. It's a new fundamental theorem of arithmetic and academia is 11 years late. ⬇️<a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#decompwlj</a> <a href="https://mathstodon.xyz/tags/FundamentalTheoremOfArithmetic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#FundamentalTheoremOfArithmetic</a> <a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sequences</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PrimeNumbers</a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JavaScript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#classification</a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#primes</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#webGL</a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#integer</a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#decomposition</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theory</a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#equation</a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graphs</a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sieve</a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fundamental</a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theorem</a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#arithmetic</a> <a href="https://mathstodon.xyz/tags/NSA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NSA</a> <a href="https://mathstodon.xyz/tags/CIA" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CIA</a> <a href="https://mathstodon.xyz/tags/DGSE" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DGSE</a> <a href="https://mathstodon.xyz/tags/DGSI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#DGSI</a> <a href="https://mathstodon.xyz/tags/Google" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Google</a>

Rémi Eismann<a href="https://mathstodon.xyz/tags/decompwlj" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#decompwlj</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.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).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.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.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.➡️ <a href="https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump</a><a href="https://mathstodon.xyz/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mathstodon.xyz/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#maths</a> <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> <a href="https://mathstodon.xyz/tags/sequences" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sequences</a> <a href="https://mathstodon.xyz/tags/OEIS" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OEIS</a> <a href="https://mathstodon.xyz/tags/NumberTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#NumberTheory</a> <a href="https://mathstodon.xyz/tags/PrimeNumbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PrimeNumbers</a> <a href="https://mathstodon.xyz/tags/JavaScript" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#JavaScript</a> <a href="https://mathstodon.xyz/tags/php" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#php</a> <a href="https://mathstodon.xyz/tags/graph" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graph</a> <a href="https://mathstodon.xyz/tags/3D" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#3D</a> <a href="https://mathstodon.xyz/tags/classification" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#classification</a> <a href="https://mathstodon.xyz/tags/primes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#primes</a> <a href="https://mathstodon.xyz/tags/threejs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#threejs</a> <a href="https://mathstodon.xyz/tags/webGL" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#webGL</a> <a href="https://mathstodon.xyz/tags/integer" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#integer</a> <a href="https://mathstodon.xyz/tags/decomposition" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#decomposition</a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#arithmetic</a> <a href="https://mathstodon.xyz/tags/numbers" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#numbers</a> <a href="https://mathstodon.xyz/tags/theory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theory</a> <a href="https://mathstodon.xyz/tags/equation" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#equation</a> <a href="https://mathstodon.xyz/tags/graphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#graphs</a> <a href="https://mathstodon.xyz/tags/sieve" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#sieve</a> <a href="https://mathstodon.xyz/tags/fundamental" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#fundamental</a> <a href="https://mathstodon.xyz/tags/theorem" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#theorem</a> <a href="https://mathstodon.xyz/tags/arithmetic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#arithmetic</a>

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