decompwlj 3D

Numbers k such that k/6^m == 2 (mod 6), where 6^m is the greatest power of 6 that divides k

A277568 on the OEIS · family residue class

Weight–level plate of Numbers k such that k/6^m == 2 (mod 6), where 6^m is the greatest power of 6 that divides k
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 viewerA277568 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L18,822 · 18.82 %
Weight class, k ≤ L81,176 · 81.18 %
Ties, k = L1
On the level line L = 11
Forced level, l ≤ d²5
Range of a(n)2 … 499,994
Range of the jump d2 … 6
Largest weight k, level L249,989, 99,980

The gaps are 2, 4 and 6; the level share is 18.82 %; L = 2 holds 58 % 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.