decompwlj 3D

Primes having only {2, 3, 5} as digits

A214703 on the OEIS · family primes

Weight–level plate of Primes having only {2, 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 viewerA214703 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,983
Level class, k > L38,283 · 38.29 %
Weight class, k ≤ L61,700 · 61.71 %
Ties, k = L0
On the level line L = 15,989
Forced level, l ≤ d²2,889
Range of a(n)2 … 23,553,232,325,333
Range of the jump d1 … 16,666,666,670,070
Largest weight k, level L23,553,225,318,313, 2,139,395,668,683

4,028 different gaps occur, from 1 to 16,666,666,670,070; the level share is 38.29 %; 2.9 % of terms are forced level (l <= d^2); there are no ties; 17 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.