decompwlj 3D

Numbers that contain a digit 0

A011540 on the OEIS · family digit rule · also known as Numbers with a digit 0

Weight–level plate of Numbers that contain a digit 0
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 viewerA011540 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L8,764 · 8.76 %
Weight class, k ≤ L91,233 · 91.24 %
Ties, k = L22
On the level line L = 17,168
Forced level, l ≤ d²8
Range of a(n)0 … 253,503
Range of the jump d1 … 10
Largest weight k, level L253,501, 126,751

Numbers with at least one digit 0; starts at a(1) = 0. Only the gaps 1 and 10 occur here, and the level class lies on the two lines L = 1 and L = 10. The level share is 8.76 %.

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.