Primes that are the sum of 11 consecutive primes
Open in the 3-D viewerA127340 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,999 |
| Level class, k > L | 56,196 · 56.20 % |
| Weight class, k ≤ L | 43,803 · 43.80 % |
| Ties, k = L | 6 |
| On the level line L = 1 | 7,998 |
| Forced level, l ≤ d² | 2,738 |
| Range of a(n) | 233 … 146,838,719 |
| Range of the jump d | 38 … 22,110 |
| Largest weight k, level L | 146,833,867, 1,479,789 |
4,020 different gaps occur, from 38 to 22,110; the level share is 56.20 %; 2.7 % 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.