decompwlj 3D

Numbers n such that m = floor(n/6) is coprime to n and, if nonzero, m is also a term of the sequence

A250048 on the OEIS · family self-referential

Weight–level plate of Numbers n such that m = floor(n/6) is coprime to n and, if nonzero, m is also a term of the sequence
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 viewerA250048 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,992
Level class, k > L8,633 · 8.63 %
Weight class, k ≤ L91,359 · 91.37 %
Ties, k = L13
On the level line L = 16,496
Forced level, l ≤ d²174
Range of a(n)1 … 3,202,691
Range of the jump d1 … 1,175,732
Largest weight k, level L3,202,679, 1,601,343

39 different gaps occur, from 1 to 1,175,732; the level share is 8.63 %; L = 1 holds 75 % of the level class; 8 terms do not decompose.

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.