Primes congruent to 7 mod 41
Open in the 3-D viewerA142204 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 49,800 · 49.80 % |
| Weight class, k ≤ L | 50,197 · 50.20 % |
| Ties, k = L | 0 |
| On the level line L = 1 | 6,082 |
| Forced level, l ≤ d² | 1,035 |
| Range of a(n) | 7 … 67,772,597 |
| Range of the jump d | 82 … 6,806 |
| Largest weight k, level L | 67,762,921, 807,543 |
68 different gaps occur, from 82 to 6,806; the level share is 49.80 %; 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.