decompwlj 3D

Primes with only nonprime decimal digits

A034844 on the OEIS · family primes

Weight–level plate of Primes with only nonprime decimal 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 viewerA034844 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L34,642 · 34.64 %
Weight class, k ≤ L65,350 · 65.36 %
Ties, k = L3
On the level line L = 19,054
Forced level, l ≤ d²1,104
Range of a(n)11 … 114,664,681
Range of the jump d2 … 20,000,062
Largest weight k, level L114,660,829, 38,216,229

792 different gaps occur, from 2 to 20,000,062; the level share is 34.64 %; 1.1 % of terms are forced level (l <= d^2); 8 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.