decompwlj 3D

Numbers that are congruent to {2, 8} mod 10

A090772 on the OEIS · family residue class

Weight–level plate of Numbers that are congruent to {2, 8} mod 10
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 viewerA090772 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L18,899 · 18.90 %
Weight class, k ≤ L81,098 · 81.10 %
Ties, k = L1
On the level line L = 10
Forced level, l ≤ d²4
Range of a(n)2 … 499,998
Range of the jump d4 … 6
Largest weight k, level L249,973, 83,329

The gaps are 4 and 6; the level share is 18.90 %; L = 2 holds 58 % 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.