decompwlj 3D

The nonnegative even numbers: a(n) = 2n

A005843 on the OEIS · family arithmetic progression · also known as Even numbers

Weight–level plate of The nonnegative even numbers: a(n) = 2n
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 viewerA005843 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,997
Level class, k > L9,593 · 9.59 %
Weight class, k ≤ L90,404 · 90.41 %
Ties, k = L1
On the level line L = 11
Forced level, l ≤ d²1
Range of a(n)0 … 199,998
Range of the jump d2 … 2
Largest weight k, level L99,991, 66,664

d = 2 and l = a - 2 = 2m. The level class is exactly {a : m an odd prime}, all on the line L = 2, plus a = 6 (L = 1) and a = 10: the naturals' level line, moved from L = 1 to L = 2 (9.59 % level, the same share).

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.