decompwlj 3D

Odd composite numbers congruent to 4 modulo 9

A247678 on the OEIS · family residue class

Weight–level plate of Odd composite numbers congruent to 4 modulo 9
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 viewerA247678 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L39,284 · 39.28 %
Weight class, k ≤ L60,715 · 60.72 %
Ties, k = L49
On the level line L = 123,109
Forced level, l ≤ d²35
Range of a(n)49 … 2,310,655
Range of the jump d18 … 90
Largest weight k, level L2,310,547, 121,585

5 different gaps occur, from 18 to 90; the level share is 39.28 %; L = 1 holds 59 % 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.