decompwlj 3D

Numbers congruent to {2, 4, 8, 16} (mod 20)

A002081 on the OEIS · family residue class

Weight–level plate of Numbers congruent to {2, 4, 8, 16} (mod 20)
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 viewerA002081 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,997
Level class, k > L8 · 0.01 %
Weight class, k ≤ L99,989 · 99.99 %
Ties, k = L1
On the level line L = 11
Forced level, l ≤ d²5
Range of a(n)2 … 499,996
Range of the jump d2 … 8
Largest weight k, level L10, 166,660

The gaps are 2, 4, 6 and 8; the level share is 0.01 %.

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.