decompwlj 3D

Numbers k such that k/10^m == 1 mod 10, where 10^m is the greatest power of 10 that divides n

A277588 on the OEIS · family residue class

Weight–level plate of Numbers k such that k/10^m == 1 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 viewerA277588 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L30,214 · 30.21 %
Weight class, k ≤ L69,784 · 69.79 %
Ties, k = L91
On the level line L = 117,773
Forced level, l ≤ d²7
Range of a(n)1 … 899,991
Range of the jump d1 … 10
Largest weight k, level L899,981, 299,903

The gaps are 1, 9 and 10; the level share is 30.21 %; L = 1 holds 59 % 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.