decompwlj 3D

Primes having only {4, 6, 9} as digits

A107666 on the OEIS · family primes

Weight–level plate of Primes having only {4, 6, 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 viewerA107666 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,989
Level class, k > L40,428 · 40.43 %
Weight class, k ≤ L59,561 · 59.57 %
Ties, k = L0
On the level line L = 16,246
Forced level, l ≤ d²3,068
Range of a(n)449 … 49,464,466,944,449
Range of the jump d20 … 34,444,444,448,220
Largest weight k, level L49,464,466,669,339, 2,354,595,235,449

3,935 different gaps occur, from 20 to 34,444,444,448,220; the level share is 40.43 %; 3.1 % of terms are forced level (l <= d^2); there are no ties; 11 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.