Numbers k for which A003961(k) < 2*k; Numbers n such that if n = product_{k >= 1} (p_k)^(c_k), then product_{k >= 1} (p_{k+1})^(c_k) < 2*n, where p_k indicates the k-th prime, A000040(k)
Open in the 3-D viewerA246281 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,996 |
| Level class, k > L | 9,192 · 9.19 % |
| Weight class, k ≤ L | 90,804 · 90.81 % |
| Ties, k = L | 72 |
| On the level line L = 1 | 7,587 |
| Forced level, l ≤ d² | 2 |
| Range of a(n) | 1 … 214,631 |
| Range of the jump d | 1 … 10 |
| Largest weight k, level L | 214,607, 107,310 |
10 different gaps occur, from 1 to 10; the level share is 9.19 %; L = 1 holds 83 % of the level class.
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.