decompwlj 3D

Primes without {2, 5} as digits

A361822 on the OEIS · family primes

Weight–level plate of Primes without {2, 5} 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 viewerA361822 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L24,195 · 24.20 %
Weight class, k ≤ L75,797 · 75.80 %
Ties, k = L9
On the level line L = 17,292
Forced level, l ≤ d²241
Range of a(n)3 … 6,411,191
Range of the jump d2 … 1,000,024
Largest weight k, level L6,411,137, 2,136,895

206 different gaps occur, from 2 to 1,000,024; the level share is 24.20 %; L = 1 holds 30 % of the level class; 8 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.