decompwlj 3D

Numbers whose smallest prime factor is 11

A084969 on the OEIS · family multiplicative

Weight–level plate of Numbers whose smallest prime factor is 11
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 viewerA084969 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L14,773 · 14.77 %
Weight class, k ≤ L85,226 · 85.23 %
Ties, k = L1
On the level line L = 15
Forced level, l ≤ d²61
Range of a(n)11 … 4,812,467
Range of the jump d22 … 110
Largest weight k, level L437,471, 209,055

5 different gaps occur, from 22 to 110; the level share is 14.77 %; L = 33 holds 38 % of the level class.

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.