decompwlj 3D

Primes containing at least one of the following digits: 4, 6, 8, or 9

A329106 on the OEIS · family primes

Weight–level plate of Primes containing at least one of the following digits: 4, 6, 8, or 9
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 viewerA329106 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L23,379 · 23.38 %
Weight class, k ≤ L76,620 · 76.62 %
Ties, k = L10
On the level line L = 17,513
Forced level, l ≤ d²16
Range of a(n)19 … 1,405,823
Range of the jump d2 … 168
Largest weight k, level L1,405,751, 468,509

68 different gaps occur, from 2 to 168; the level share is 23.38 %; L = 1 holds 32 % of the level class.

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.