decompwlj 3D

Positive integers congruent to 2 (mod 4): a(n) = 4*n+2, for n >= 0

A016825 on the OEIS · family residue class

Weight–level plate of Positive integers congruent to 2 (mod 4): a(n) = 4*n+2, for n >= 0
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 viewerA016825 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,998
Level class, k > L17,983 · 17.98 %
Weight class, k ≤ L82,015 · 82.02 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²3
Range of a(n)2 … 399,998
Range of the jump d4 … 4
Largest weight k, level L199,967, 79,998

The gap is always 4; the level share is 17.98 %; L = 2 holds 100 % 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.