decompwlj 3D

Primes having only 0,4,6,8,9 as digits

A061372 on the OEIS · family primes

Weight–level plate of Primes having only 0,4,6,8,9 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 viewerA061372 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,991
Level class, k > L39,052 · 39.06 %
Weight class, k ≤ L60,939 · 60.94 %
Ties, k = L1
On the level line L = 17,649
Forced level, l ≤ d²1,995
Range of a(n)89 … 6,088,084,649
Range of the jump d10 … 3,000,001,140
Largest weight k, level L6,088,046,369, 553,358,589

1,398 different gaps occur, from 10 to 3,000,001,140; the level share is 39.06 %; 2.0 % of terms are forced level (l <= d^2); 9 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.