Primes having only {6, 7, 8, 9} as digits
Open in the 3-D viewerA106111 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,990 |
| Level class, k > L | 27,675 · 27.68 % |
| Weight class, k ≤ L | 72,315 · 72.32 % |
| Ties, k = L | 1 |
| On the level line L = 1 | 4,773 |
| Forced level, l ≤ d² | 785 |
| Range of a(n) | 7 … 67,886,799,779 |
| Range of the jump d | 2 … 56,666,666,700 |
| Largest weight k, level L | 67,886,796,517, 22,628,928,965 |
793 different gaps occur, from 2 to 56,666,666,700; the level share is 27.68 %; 10 terms do not decompose.
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.