Products (semiprimes) of two distinct safe primes
Open in the 3-D viewerA157352 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,999 |
| Level class, k > L | 49,966 · 49.97 % |
| Weight class, k ≤ L | 50,033 · 50.03 % |
| Ties, k = L | 6 |
| On the level line L = 1 | 10,807 |
| Forced level, l ≤ d² | 568 |
| Range of a(n) | 35 … 44,054,935 |
| Range of the jump d | 2 … 4,914 |
| Largest weight k, level L | 44,042,653, 14,679,277 |
1,089 different gaps occur, from 2 to 4,914; the level share is 49.97 %.
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.