Primes of the form 256n+129
Open in the 3-D viewerA105130 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,998 |
| Level class, k > L | 58,189 · 58.19 % |
| Weight class, k ≤ L | 41,809 · 41.81 % |
| Ties, k = L | 11 |
| On the level line L = 1 | 5,685 |
| Forced level, l ≤ d² | 4,071 |
| Range of a(n) | 641 … 233,685,889 |
| Range of the jump d | 256 … 20,736 |
| Largest weight k, level L | 233,651,329, 889,421 |
77 different gaps occur, from 256 to 20,736; the level share is 58.19 %; 4.1 % 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.