decompwlj 3D

Primes p such that p's set of distinct digits is {1,3,7,9}

A108386 on the OEIS · family primes

Weight–level plate of Primes p such that p's set of distinct digits is {1,3,7,9}
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 viewerA108386 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,986
Level class, k > L30,614 · 30.62 %
Weight class, k ≤ L69,372 · 69.38 %
Ties, k = L1
On the level line L = 15,957
Forced level, l ≤ d²1,779
Range of a(n)1,973 … 7,977,197,731
Range of the jump d2 … 3,111,111,588
Largest weight k, level L7,977,193,307, 2,659,057,103

2,332 different gaps occur, from 2 to 3,111,111,588; the level share is 30.62 %; 1.8 % of terms are forced level (l <= d^2); 14 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.