Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits
Open in the 3-D viewerA078972 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,997 |
| Level class, k > L | 35,068 · 35.07 % |
| Weight class, k ≤ L | 64,929 · 64.93 % |
| Ties, k = L | 7 |
| On the level line L = 1 | 8,169 |
| Forced level, l ≤ d² | 287 |
| Range of a(n) | 4 … 8,576,377 |
| Range of the jump d | 1 … 24,072 |
| Largest weight k, level L | 8,576,017, 2,856,859 |
619 different gaps occur, from 1 to 24,072; the level share is 35.07 %.
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.