decompwlj 3D

Primes without 0's or primes in their decimal expansion

A152313 on the OEIS · family primes

Weight–level plate of Primes without 0's or primes in their decimal expansion
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 viewerA152313 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,990
Level class, k > L35,561 · 35.56 %
Weight class, k ≤ L64,429 · 64.44 %
Ties, k = L1
On the level line L = 18,554
Forced level, l ≤ d²1,428
Range of a(n)11 … 869,986,699
Range of the jump d2 … 211,111,200
Largest weight k, level L869,986,657, 289,989,829

1,283 different gaps occur, from 2 to 211,111,200; the level share is 35.56 %; 1.4 % of terms are forced level (l <= d^2); 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.