decompwlj 3D

a(n) = composite(composite(n)), where composite = A002808, composite numbers

A050435 on the OEIS · family complement

Weight–level plate of a(n) = composite(composite(n)), where composite = A002808, composite 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 viewerA050435 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L10,948 · 10.95 %
Weight class, k ≤ L89,052 · 89.05 %
Ties, k = L60
On the level line L = 19,083
Forced level, l ≤ d²2
Range of a(n)9 … 121,959
Range of the jump d1 … 4
Largest weight k, level L121,951, 60,979

The gaps are 1, 2, 3 and 4; the level share is 10.95 %; L = 1 holds 83 % 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.