decompwlj 3D

Primes having only {3, 4, 9} as digits

A199349 on the OEIS · family primes

Weight–level plate of Primes having only {3, 4, 9} 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 viewerA199349 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,979
Level class, k > L32,365 · 32.37 %
Weight class, k ≤ L67,614 · 67.63 %
Ties, k = L0
On the level line L = 14,706
Forced level, l ≤ d²2,193
Range of a(n)3 … 4,493,349,439,993
Range of the jump d4 … 2,333,333,338,350
Largest weight k, level L4,493,344,344,037, 898,668,798,867

2,997 different gaps occur, from 4 to 2,333,333,338,350; the level share is 32.37 %; 2.2 % of terms are forced level (l <= d^2); there are no ties; 21 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.