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
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
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...
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decompwlj.net
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 A052499: If n is in the sequence then so are 2n and 4n-1
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A052499
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…
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 A014574: Average of twin prime pairs
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A014574
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 A061673: Even numbers k such that k+1 and k-1 are both composite
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A061673
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…
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
Decompwlj and the Great Conjectures: Opus 5.5 report: 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 A000961: Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1)
Interactive 3D/2D threejs graphs - CSV download - OEIS link ➡️ decompwlj.net/seq/A000961
Decompwlj and the Great Conjectures: Opus 5.5 report: Legendre, Andrica, Cramér, the Riemann Hypothesis, twin primes, Goldbach and Collatz where they touch
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decompwlj.com/weight-level-j…
