Decomposition into weight × level + jump - 3D graphs - 2D graphs - First 500 terms

Definitions.
Dump (sql.zip).
There are 460 sequences decomposed. 3D graphs use three.js (you must have a web browser that supports WebGL).

The decomposition into weight × level + jump is a decomposition of positive integer. 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) and the decomposition is possible if a(n+1)<3/2×a(n).

The decomposition into weight × level + jump of natural numbers is the sieve of Eratosthenes. 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 this decompositions, i apply a kind of sieve on each sequences. In some way, i find composites (numbers classified by weight ?) and primes (numbers classified by level ?) of each sequences.

All 2D graphs on one page.
Decomposition of prime numbers commented.

50 sequences decomposed into weight × level + jump in one gif

arXiv:0711.0865 : Decomposition into weight × level + jump and application to a new classification of primes
OEIS sequences submitted and/or edited
Decomposition into weight × level + jump on the OeisWiki
Google+ - Album Google+ - Twitter - Tumblr - Reddit: Nunki08 - subreddit /r/decompwlj
The On-Line Encyclopedia of Integer Sequences (OEIS) - OEIS Foundation
Rémi Eismann.