decompwlj 3D

Numbers whose smallest prime factor is 17

A332799 on the OEIS · family multiplicative

Weight–level plate of Numbers whose smallest prime factor is 17
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 viewerA332799 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L16,325 · 16.33 %
Weight class, k ≤ L83,674 · 83.67 %
Ties, k = L0
On the level line L = 16
Forced level, l ≤ d²120
Range of a(n)17 … 8,862,967
Range of the jump d34 … 374
Largest weight k, level L521,161, 253,215

10 different gaps occur, from 34 to 374; the level share is 16.33 %; L = 17 holds 36 % of the level class; 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.