decompwlj 3D

Numbers with semiprime digits (digits 4, 6, 9 only)

A107665 on the OEIS · family digit rule

Weight–level plate of Numbers with semiprime digits (digits 4, 6, 9 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 viewerA107665 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,988
Level class, k > L16,232 · 16.23 %
Weight class, k ≤ L83,756 · 83.77 %
Ties, k = L0
On the level line L = 13,941
Forced level, l ≤ d²545
Range of a(n)4 … 44,694,944,494
Range of the jump d2 … 34,444,444,445
Largest weight k, level L44,694,696,443, 14,898,314,814

30 different gaps occur, from 2 to 34,444,444,445; the level share is 16.23 %; L = 2 holds 33 % of the level class; there are no ties; 12 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.