Primes of form 5207*n + 1
Open in the 3-D viewerA163612 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 100,000 |
| Level class, k > L | 89,118 · 89.12 % |
| Weight class, k ≤ L | 10,882 · 10.88 % |
| Ties, k = L | 1 |
| On the level line L = 1 | 5,492 |
| Forced level, l ≤ d² | 59,168 |
| Range of a(n) | 437,389 … 11,158,809,281 |
| Range of the jump d | 10,414 … 1,124,712 |
| Largest weight k, level L | 11,158,340,651, 1,053,947 |
88 different gaps occur, from 10,414 to 1,124,712; the level share is 89.12 %; 59.2 % 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.