decompwlj 3D

Primes having only {2, 3, 8} as digits

A260127 on the OEIS · family primes

Weight–level plate of Primes having only {2, 3, 8} 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 viewerA260127 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,974
Level class, k > L40,313 · 40.32 %
Weight class, k ≤ L59,661 · 59.68 %
Ties, k = L0
On the level line L = 15,940
Forced level, l ≤ d²3,253
Range of a(n)2 … 23,882,283,388,333
Range of the jump d1 … 13,333,333,334,990
Largest weight k, level L23,882,283,313,313, 2,167,125,748,983

3,295 different gaps occur, from 1 to 13,333,333,334,990; the level share is 40.32 %; 3.3 % of terms are forced level (l <= d^2); there are no ties; 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.