decompwlj 3D

Primes having only {0, 1, 5} as digits

A199325 on the OEIS · family primes

Weight–level plate of Primes having only {0, 1, 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 viewerA199325 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,976
Level class, k > L39,667 · 39.68 %
Weight class, k ≤ L60,309 · 60.32 %
Ties, k = L0
On the level line L = 15,711
Forced level, l ≤ d²3,569
Range of a(n)5 … 50,110,515,510,551
Range of the jump d6 … 34,444,444,455,000
Largest weight k, level L50,110,515,505,991, 4,555,468,192,281

3,282 different gaps occur, from 6 to 34,444,444,455,000; the level share is 39.68 %; 3.6 % 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.