decompwlj 3D

Numbers k such that k/10^m == 4 mod 10, where 10^m is the greatest power of 10 that divides n

A277591 on the OEIS · family residue class

Weight–level plate of Numbers k such that k/10^m == 4 mod 10, where 10^m is the greatest power of 10 that divides n
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 viewerA277591 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L21,366 · 21.37 %
Weight class, k ≤ L78,632 · 78.63 %
Ties, k = L2
On the level line L = 11
Forced level, l ≤ d²9
Range of a(n)4 … 899,994
Range of the jump d4 … 10
Largest weight k, level L449,987, 149,956

The gaps are 4, 6 and 10; the level share is 21.37 %; L = 2 holds 44 % 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.