decompwlj 3D

Even-Lucky-Numbers: generated by a sieve process like that for Lucky numbers but starting with even numbers

A045954 on the OEIS · family sieve

Weight–level plate of Even-Lucky-Numbers: generated by a sieve process like that for Lucky numbers but starting with even numbers
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 viewerA045954 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L20,560 · 20.56 %
Weight class, k ≤ L79,436 · 79.44 %
Ties, k = L3
On the level line L = 10
Forced level, l ≤ d²6
Range of a(n)2 … 1,392,228
Range of the jump d2 … 128
Largest weight k, level L696,053, 464,006

56 different gaps occur, from 2 to 128; the level share is 20.56 %; L = 2 holds 50 % 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.