Beastly primes (version 2): primes containing 666 as a substring
Open in the 3-D viewerA131645 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 32,646 · 32.65 % |
| Weight class, k ≤ L | 67,351 · 67.35 % |
| Ties, k = L | 1 |
| On the level line L = 1 | 5,853 |
| Forced level, l ≤ d² | 13,221 |
| Range of a(n) | 6,661 … 411,666,511 |
| Range of the jump d | 2 … 110,000 |
| Largest weight k, level L | 411,666,487, 137,222,139 |
759 different gaps occur, from 2 to 110,000; the level share is 32.65 %; 13.2 % of terms are forced level (l <= d^2).
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.