decompwlj 3D

Primes having only {0, 6, 8, 9} as digits

A053580 on the OEIS · family primes

Weight–level plate of Primes having only {0, 6, 8, 9} as digits
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 viewerA053580 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L38,723 · 38.73 %
Weight class, k ≤ L61,268 · 61.27 %
Ties, k = L0
On the level line L = 18,006
Forced level, l ≤ d²2,206
Range of a(n)89 … 98,688,008,669
Range of the jump d10 … 50,000,001,000
Largest weight k, level L98,686,999,429, 8,971,528,089

2,465 different gaps occur, from 10 to 50,000,001,000; the level share is 38.73 %; 2.2 % of terms are forced level (l <= d^2); 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.