Primes congruent to 3 or 7 mod 20
Open in the 3-D viewerA122870 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 37,240 · 37.24 % |
| Weight class, k ≤ L | 62,757 · 62.76 % |
| Ties, k = L | 0 |
| On the level line L = 1 | 9,734 |
| Forced level, l ≤ d² | 63 |
| Range of a(n) | 3 … 5,795,507 |
| Range of the jump d | 4 … 564 |
| Largest weight k, level L | 5,794,787, 826,917 |
71 different gaps occur, from 4 to 564; the level share is 37.24 %; 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.