decompwlj 3D

Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8

A047422 on the OEIS · family residue class

Weight–level plate of Numbers that are congruent to {1, 2, 3, 4, 5, 6} mod 8
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 viewerA047422 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L10,483 · 10.48 %
Weight class, k ≤ L89,514 · 89.52 %
Ties, k = L72
On the level line L = 19,349
Forced level, l ≤ d²0
Range of a(n)1 … 133,332
Range of the jump d1 … 3
Largest weight k, level L133,321, 66,665

The gaps are 1 and 3; the level share is 10.48 %; L = 1 holds 89 % of the level class.

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.