decompwlj 3D

Primes having only {4, 5, 7} as digits

A217039 on the OEIS · family primes

Weight–level plate of Primes having only {4, 5, 7} 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 viewerA217039 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,987
Level class, k > L37,422 · 37.43 %
Weight class, k ≤ L62,565 · 62.57 %
Ties, k = L0
On the level line L = 15,738
Forced level, l ≤ d²2,231
Range of a(n)5 … 47,444,555,457,757
Range of the jump d2 … 36,666,666,677,800
Largest weight k, level L47,444,554,775,147, 4,161,594,977,067

4,163 different gaps occur, from 2 to 36,666,666,677,800; the level share is 37.43 %; 2.2 % of terms are forced level (l <= d^2); there are no ties; 13 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.