Primes congruent to 6 mod 41
Open in the 3-D viewerA142203 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 50,303 · 50.30 % |
| Weight class, k ≤ L | 49,694 · 49.70 % |
| Ties, k = L | 0 |
| On the level line L = 1 | 6,183 |
| Forced level, l ≤ d² | 1,048 |
| Range of a(n) | 47 … 67,882,517 |
| Range of the jump d | 82 … 7,790 |
| Largest weight k, level L | 67,871,119, 801,843 |
68 different gaps occur, from 82 to 7,790; the level share is 50.30 %; 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.