Primes congruent to 39 mod 55
Open in the 3-D viewerA142629 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,998 |
| Level class, k > L | 54,731 · 54.73 % |
| Weight class, k ≤ L | 45,267 · 45.27 % |
| Ties, k = L | 0 |
| On the level line L = 1 | 9,615 |
| Forced level, l ≤ d² | 1,000 |
| Range of a(n) | 149 … 67,825,049 |
| Range of the jump d | 110 … 5,940 |
| Largest weight k, level L | 67,822,189, 608,559 |
51 different gaps occur, from 110 to 5,940; the level share is 54.73 %; 1.0 % 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.