decompwlj 3D

Primes containing only digits from the set (0,1,2,3,4)

A036956 on the OEIS · family primes

Weight–level plate of Primes containing only digits from the set (0,1,2,3,4)
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 viewerA036956 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,989
Level class, k > L28,799 · 28.80 %
Weight class, k ≤ L71,190 · 71.20 %
Ties, k = L3
On the level line L = 15,813
Forced level, l ≤ d²1,035
Range of a(n)2 … 433,334,023
Range of the jump d1 … 55,555,802
Largest weight k, level L433,331,219, 144,433,733

507 different gaps occur, from 1 to 55,555,802; the level share is 28.80 %; 1.0 % of terms are forced level (l <= d^2); 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.