@decompwlj

I invented the decomposition into weight × level + jump, an extension to the fundamental theorem of arithmetic and a new way to see the numbers. #decompwlj

 France
oeis.org/wiki/User:R%C3%A9mi_Eismann
Joined December 2013
  • Tweets18K
  • Following2.2K
  • Followers947
14.5KMedia
#decompwlj OEISWiki (en) ➡️ oeis.org/wiki/Decomposition_… Wikiversité (fr) ➡️ fr.wikiversity.org/wiki/Rech… arXiv [math.NT] ➡️ arxiv.org/abs/0711.0865 1000 seq decomposed but my data have not been verified (dump, img and csv zipped) ➡️ decompwlj.com
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decompwlj 3D: 5000 OEIS integer sequences decomposed into weight × level + jump with interactive 3D/2D three.js graphs - CSV exports - OEIS link - compare sequences - similar sequences... ➡️ decompwlj.net
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Decomposition into weight × level + jump of OEIS sequence A034837: Numbers that are divisible by the first, i.e., the leftmost, digit Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A034837
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The decomposition into weight × level + jump of natural numbers is the sieve of Eratosthenes
Graph - 2D (log(weight),log(level)): decomposition into weight × level + jump of natural numbers: the sieve of Eratosthenes

ALT Graph - 2D (log(weight),log(level)): decomposition into weight × level + jump of natural numbers: the sieve of Eratosthenes

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Opus 5.5 report: Decompwlj and the Great Conjectures: Legendre, Andrica, Cramér, the Riemann Hypothesis, twin primes, Goldbach and Collatz where they touch ⬇️ decompwlj.com/weight-level-j…

Decompwlj and the Great Conjectures

Where Legendre, Andrica, Cramér, RH, twin primes, Goldbach and Collatz really touch the weight × level + jump decomposition. Eight pages, every number recomputed, PARI/GP included.

decompwlj.com
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Decomposition into weight × level + jump of OEIS sequence A001597: Perfect powers: m^k where m > 0 and k >= 2 Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A001597
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decompwlj 3D: 5000 OEIS integer sequences decomposed into weight × level + jump with interactive 3D/2D three.js graphs - CSV exports - OEIS link - compare sequences - similar sequences... ➡️ decompwlj.net
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Decomposition into weight × level + jump of OEIS sequence A035005: Number of possible queen moves on an n X n chessboard Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A035005
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Opus 5.5: A six-page introduction for Graduates to the decomposition into weight × level + jump of increasing integer sequences, with the primes as the main application. ⬇️ decompwlj.com/weight-level-j…

Weight × Level + Jump — a six-page introduction

One canonical change of coordinates for increasing sequences. On ℕ it is the sieve of Eratosthenes; on the primes, weight 3 is the twin column and the level class has density zero.

decompwlj.com
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50 OEIS sequences decomposed into weight × level + jump (log(weight),log(level)) 5000 sequences decomposed with interactive 3D/2D three.js graphs, CSV exports,OEIS link... ➡️ decompwlj.net
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Decomposition into weight × level + jump of OEIS sequence A002476: Primes of the form 6m + 1 Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A002476
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The decomposition into weight × level + jump of natural numbers is the sieve of Eratosthenes
Graph - 2D (log(weight),log(level)): decomposition into weight × level + jump of natural numbers: the sieve of Eratosthenes

ALT Graph - 2D (log(weight),log(level)): decomposition into weight × level + jump of natural numbers: the sieve of Eratosthenes

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In the decomposition of prime numbers into weight × level + jump, the Twin Prime Conjecture becomes: there are infinitely many primes with weight 3
Graph - 3D three.js: decomposition of prime numbers into weight × level + jump with a highlight on lesser of twin primes

ALT Graph - 3D three.js: decomposition of prime numbers into weight × level + jump with a highlight on lesser of twin primes

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decompwlj of OEIS sequence A007378: a(n), for n >= 2, is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A007378
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Decomposition into weight × level + jump of OEIS sequence A002145: Primes of the form 4*k + 3 Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A002145
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decompwlj 3D: 5000 OEIS integer sequences decomposed into weight × level + jump with interactive 3D/2D three.js graphs - CSV exports - OEIS link - compare sequences - similar sequences... ➡️ decompwlj.net
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Decomposition into weight × level + jump of OEIS sequence A005244: A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence Interactive 3D/2D threejs graphs - OEIS link ➡️ decompwlj.net/seq/A005244
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50 OEIS sequences decomposed into weight × level + jump (log(weight),log(level)) 5000 sequences decomposed with interactive 3D/2D three.js graphs, CSV exports,OEIS link... ➡️ decompwlj.net
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Decomposition into weight × level + jump of OEIS sequence A004743: Numbers whose binary expansion does not contain 110 Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A004743
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decompwlj 3D: 5000 OEIS integer sequences decomposed into weight × level + jump with interactive 3D/2D three.js graphs - CSV exports - OEIS link - compare sequences - similar sequences... ➡️ decompwlj.net
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Decomposition into weight × level + jump of OEIS sequence A081330: Numbers that can be written as sum of two 3-smooth numbers Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A081330
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