decompwlj 3D

Primes without {1, 9} as digits

A154761 on the OEIS · family primes

Weight–level plate of Primes without {1, 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 viewerA154761 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,990
Level class, k > L32,638 · 32.64 %
Weight class, k ≤ L67,352 · 67.36 %
Ties, k = L5
On the level line L = 19,555
Forced level, l ≤ d²291
Range of a(n)2 … 22,358,543
Range of the jump d1 … 11,111,236
Largest weight k, level L22,356,491, 3,193,347

275 different gaps occur, from 1 to 11,111,236; the level share is 32.64 %; 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.