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
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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
The decomposition into weight × level + jump of natural numbers is the sieve of Eratosthenes
ALT Graph - 2D (log(weight),log(level)): decomposition into weight × level + jump of natural numbers: the sieve of Eratosthenes
In the decomposition of prime numbers into weight × level + jump, the Twin Prime Conjecture becomes: there are infinitely many primes with weight 3
ALT Graph - 3D three.js: decomposition of prime numbers into weight × level + jump with a highlight on lesser of twin primes
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
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
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
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
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
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
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
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
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.
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decompwlj.com/weight-level-j…
Opus 5.5 report: Decompwlj and the Great Conjectures: Legendre, Andrica, Cramér, the Riemann Hypothesis, twin primes, Goldbach and Collatz where they touch
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decompwlj.com/weight-level-j…
Decomposition into weight × level + jump of OEIS sequence A007950: Binary sieve: delete every 2nd number, then every 4th, 8th, etc
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A007950
Decomposition into weight × level + jump of Multiples. A short thread 🧵
A005843: The nonnegative even numbers: a(n) = 2n
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
Decomposition into weight × level + jump of OEIS sequence A173626: Primes p such that p-1 has no prime factors larger than sqrt(p)
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A173626