Primes that are sum of five consecutive primes
Open in the 3-D viewerA034965 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 100,000 |
| Level class, k > L | 49,665 · 49.66 % |
| Weight class, k ≤ L | 50,335 · 50.34 % |
| Ties, k = L | 8 |
| On the level line L = 1 | 8,424 |
| Forced level, l ≤ d² | 869 |
| Range of a(n) | 53 … 55,978,393 |
| Range of the jump d | 14 … 8,088 |
| Largest weight k, level L | 55,975,999, 1,808,559 |
1,817 different gaps occur, from 14 to 8,088; the level share is 49.66 %.
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.