decompwlj 3D

Primes that contain only the digits (2, 5, 7)

A214705 on the OEIS · family primes

Weight–level plate of Primes that contain only the digits (2, 5, 7)
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 viewerA214705 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,976
Level class, k > L40,977 · 40.99 %
Weight class, k ≤ L58,999 · 59.01 %
Ties, k = L0
On the level line L = 16,344
Forced level, l ≤ d²3,389
Range of a(n)2 … 25,775,227,257,277
Range of the jump d2 … 14,444,444,449,500
Largest weight k, level L25,775,222,767,927, 1,227,391,679,797

3,783 different gaps occur, from 2 to 14,444,444,449,500; the level share is 40.99 %; 3.4 % of terms are forced level (l <= d^2); there are no ties; 24 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.