Primes for which the weight as defined in A117078 is 9 and the gap as defined in A001223 is 8
Open in the 3-D viewerA118922 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 56,955 · 56.96 % |
| Weight class, k ≤ L | 43,042 · 43.04 % |
| Ties, k = L | 0 |
| On the level line L = 1 | 15,708 |
| Forced level, l ≤ d² | 1,476 |
| Range of a(n) | 89 … 88,526,663 |
| Range of the jump d | 18 … 10,170 |
| Largest weight k, level L | 88,517,393, 4,520,897 |
382 different gaps occur, from 18 to 10,170; the level share is 56.96 %; 1.5 % of terms are forced level (l <= d^2); there are no ties.
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.