decompwlj 3D

Primes having only {3, 4, 5} as digits

A199345 on the OEIS · family primes

Weight–level plate of Primes having only {3, 4, 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 viewerA199345 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,985
Level class, k > L36,722 · 36.73 %
Weight class, k ≤ L63,263 · 63.27 %
Ties, k = L0
On the level line L = 15,721
Forced level, l ≤ d²2,671
Range of a(n)3 … 35,335,443,435,443
Range of the jump d2 … 27,777,777,780,890
Largest weight k, level L35,335,434,541,573, 3,212,304,949,503

1,276 different gaps occur, from 2 to 27,777,777,780,890; the level share is 36.73 %; 2.7 % of terms are forced level (l <= d^2); there are no ties; 15 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.