decompwlj 3D

Numbers containing the digits 0, 1, 2, 5 or 8 only

A080228 on the OEIS · family digit rule

Weight–level plate of Numbers containing the digits 0, 1, 2, 5 or 8 only
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 viewerA080228 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,990
Level class, k > L14,615 · 14.62 %
Weight class, k ≤ L85,375 · 85.38 %
Ties, k = L21
On the level line L = 16,823
Forced level, l ≤ d²298
Range of a(n)0 … 11,188,888
Range of the jump d1 … 2,111,112
Largest weight k, level L11,188,049, 5,594,440

15 different gaps occur, from 1 to 2,111,112; the level share is 14.62 %; L = 1 holds 47 % of the level class; 10 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.