decompwlj 3D

Numbers without the decimal digits 1, 3, 5 and 7

A276138 on the OEIS · family digit rule

Weight–level plate of Numbers without the decimal digits 1, 3, 5 and 7
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 viewerA276138 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L12,934 · 12.94 %
Weight class, k ≤ L87,057 · 87.06 %
Ties, k = L0
On the level line L = 13,044
Forced level, l ≤ d²229
Range of a(n)0 … 4,090,986
Range of the jump d1 … 1,000,001
Largest weight k, level L4,090,967, 2,045,449

8 different gaps occur, from 1 to 1,000,001; the level share is 12.94 %; L = 2 holds 65 % of the level class; there are no ties; 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.