decompwlj 3D

Numbers n such that m = floor(n/7) is not coprime to n and, if nonzero, m is also a term of the sequence

A250047 on the OEIS · family self-referential

Weight–level plate of Numbers n such that m = floor(n/7) is not coprime to n and, if nonzero, m is also a term of the sequence
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA250047 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L11,238 · 11.24 %
Weight class, k ≤ L88,754 · 88.76 %
Ties, k = L25
On the level line L = 13,690
Forced level, l ≤ d²292
Range of a(n)2 … 4,102,478
Range of the jump d1 … 823,544
Largest weight k, level L4,102,393, 2,051,212

22 different gaps occur, from 1 to 823,544; the level share is 11.24 %; L = 2 holds 41 % of the level class; 8 terms do not decompose.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.