decompwlj 3D

Numbers congruent to {17, 23} mod 30

A267984 on the OEIS · family residue class

Weight–level plate of Numbers congruent to {17, 23} mod 30
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 viewerA267984 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L36,771 · 36.77 %
Weight class, k ≤ L63,228 · 63.23 %
Ties, k = L0
On the level line L = 128,563
Forced level, l ≤ d²20
Range of a(n)17 … 1,499,993
Range of the jump d6 … 24
Largest weight k, level L1,499,921, 214,283

The gaps are 6 and 24; the level share is 36.77 %; L = 1 holds 78 % 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.