decompwlj 3D

Even numbers n>=6 for which lpf(n-1) > lpf(n-3), where lpf = least prime factor

A243937 on the OEIS · family multiplicative

Weight–level plate of Even numbers n>=6 for which lpf(n-1) > lpf(n-3), where lpf = least prime factor
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 viewerA243937 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L15,143 · 15.14 %
Weight class, k ≤ L84,856 · 84.86 %
Ties, k = L2
On the level line L = 11
Forced level, l ≤ d²4
Range of a(n)6 … 392,592
Range of the jump d2 … 6
Largest weight k, level L196,277, 98,146

The gaps are 2, 4 and 6; the level share is 15.14 %; L = 2 holds 61 % 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.