decompwlj 3D

Numbers that are congruent to {3,9,15,18,21} mod 24

A259754 on the OEIS · family residue class

Weight–level plate of Numbers that are congruent to {3,9,15,18,21} mod 24
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 viewerA259754 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L14,672 · 14.67 %
Weight class, k ≤ L85,326 · 85.33 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²3
Range of a(n)3 … 479,997
Range of the jump d3 … 6
Largest weight k, level L159,977, 119,997

The gaps are 3 and 6; the level share is 14.67 %; L = 3 holds 100 % of the level class; there are no ties.

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.