Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x+1 are in S
Open in the 3-D viewerA147991 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 9,321 · 9.32 % |
| Weight class, k ≤ L | 90,676 · 90.68 % |
| Ties, k = L | 1 |
| On the level line L = 1 | 16 |
| Forced level, l ≤ d² | 564 |
| Range of a(n) | 1 … 50,383,499 |
| Range of the jump d | 1 … 14,348,908 |
| Largest weight k, level L | 21,523,359, 16,794,499 |
17 different gaps occur, from 1 to 14,348,908; the level share is 9.32 %; L = 3 holds 62 % 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.