Lower prime of a difference of 18 between consecutive primes
Open in the 3-D viewerA031936 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,999 |
| Level class, k > L | 43,055 · 43.06 % |
| Weight class, k ≤ L | 56,944 · 56.94 % |
| Ties, k = L | 5 |
| On the level line L = 1 | 8,097 |
| Forced level, l ≤ d² | 397 |
| Range of a(n) | 523 … 23,818,099 |
| Range of the jump d | 18 … 2,768 |
| Largest weight k, level L | 23,817,883, 1,253,047 |
819 different gaps occur, from 18 to 2,768; the level share is 43.06 %.
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.