decompwlj 3D

Primes having only {1, 3, 5} as digits

A260224 on the OEIS · family primes

Weight–level plate of Primes having only {1, 3, 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 viewerA260224 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,974
Level class, k > L32,491 · 32.50 %
Weight class, k ≤ L67,483 · 67.50 %
Ties, k = L1
On the level line L = 14,163
Forced level, l ≤ d²2,525
Range of a(n)3 … 3,331,515,335,153
Range of the jump d2 … 1,555,555,555,782
Largest weight k, level L3,331,513,551,713, 1,110,504,517,043

1,215 different gaps occur, from 2 to 1,555,555,555,782; the level share is 32.50 %; 2.5 % of terms are forced level (l <= d^2); 26 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.