Primes congruent to 31 mod 49
Open in the 3-D viewerA142440 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,996 |
| Level class, k > L | 52,041 · 52.04 % |
| Weight class, k ≤ L | 47,955 · 47.96 % |
| Ties, k = L | 0 |
| On the level line L = 1 | 7,335 |
| Forced level, l ≤ d² | 1,115 |
| Range of a(n) | 31 … 71,385,191 |
| Range of the jump d | 98 … 6,566 |
| Largest weight k, level L | 71,377,253, 719,057 |
59 different gaps occur, from 98 to 6,566; the level share is 52.04 %; 1.1 % 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.