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
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
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…
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
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
Decomposition into weight × level + jump of OEIS sequence A032810: Numbers using only digits 2 and 3
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A032810
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 A014190: Palindromes in base 3 (written in base 10)
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A014190
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…
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 A008586: Multiples of 4
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A008586
3 sequences with nice, different graphs. A mini thread 🧵
A014312: Numbers with exactly 4 ones in binary expansion
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A014312
A027469: a(n) = 49*(n-1)*(n-2)/2
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A027469
A044102: Multiples of 36
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A044102
Decomposition into weight × level + jump of some smooth numbers. A mini thread 🧵
A051038: 11-smooth numbers: numbers whose prime divisors are all <= 11
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A051038
A080681: 17-smooth numbers: numbers whose prime divisors are all <= 17
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A080681
A080682: 19-smooth numbers: numbers whose prime divisors are all <= 19
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A080682