decompwlj 3D

1 and the prime powers p^m where m >= 2, thus excluding the primes

A025475 on the OEIS · family powers

Weight–level plate of 1 and the prime powers p^m where m >= 2, thus excluding the primes
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA025475 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L99,968 · 99.97 %
Weight class, k ≤ L27 · 0.03 %
Ties, k = L0
On the level line L = 117,626
Forced level, l ≤ d²99,878
Range of a(n)1 … 1,623,863,427,481
Range of the jump d1 … 238,596,672
Largest weight k, level L1,623,827,746,633, 67,766,877

95,090 different gaps occur, from 1 to 238,596,672; the level share is 99.97 %; 99.9 % of terms are forced level (l <= d^2); there are no ties.

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.