Prime self (or Colombian) numbers: primes not expressible as the sum of an integer and its digit sum
Open in the 3-D viewerA006378 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,995 |
| Level class, k > L | 41,703 · 41.71 % |
| Weight class, k ≤ L | 58,292 · 58.29 % |
| Ties, k = L | 3 |
| On the level line L = 1 | 8,592 |
| Forced level, l ≤ d² | 249 |
| Range of a(n) | 3 … 16,503,797 |
| Range of the jump d | 2 … 1,712 |
| Largest weight k, level L | 16,501,817, 5,489,879 |
259 different gaps occur, from 2 to 1,712; the level share is 41.71 %.
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.