decompwlj 3D

Numbers without the decimal digits 2, 4, 6 and 8

A276137 on the OEIS · family digit rule

Weight–level plate of Numbers without the decimal digits 2, 4, 6 and 8
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 viewerA276137 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L15,529 · 15.53 %
Weight class, k ≤ L84,462 · 84.47 %
Ties, k = L32
On the level line L = 112,455
Forced level, l ≤ d²231
Range of a(n)0 … 3,090,975
Range of the jump d1 … 1,000,001
Largest weight k, level L3,090,973, 1,545,454

8 different gaps occur, from 1 to 1,000,001; the level share is 15.53 %; L = 1 holds 80 % of the level class; 9 terms do not decompose.

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.