decompwlj 3D

Primes whose digits are primes; primes having only {2, 3, 5, 7} as digits

A019546 on the OEIS · family primes

Weight–level plate of Primes whose digits are primes; primes having only {2, 3, 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 viewerA019546 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,987
Level class, k > L34,151 · 34.16 %
Weight class, k ≤ L65,836 · 65.84 %
Ties, k = L2
On the level line L = 17,331
Forced level, l ≤ d²1,472
Range of a(n)2 … 23,325,232,253
Range of the jump d1 … 14,444,444,646
Largest weight k, level L23,325,224,191, 3,331,933,903

1,942 different gaps occur, from 1 to 14,444,444,646; the level share is 34.16 %; 1.5 % of terms are forced level (l <= d^2); 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.