decompwlj 3D

Multiples of 10 containing a 10 in their decimal representation

A121030 on the OEIS · family digit rule

Weight–level plate of Multiples of 10 containing a 10 in their decimal representation
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 viewerA121030 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L24,311 · 24.31 %
Weight class, k ≤ L75,687 · 75.69 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²96
Range of a(n)10 … 6,651,020
Range of the jump d10 … 100
Largest weight k, level L665,051, 604,190

The gaps are 10, 90 and 100; the level share is 24.31 %; L = 10 holds 63 % 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.