decompwlj 3D

Numbers k such that k and k+4 are 4-almost primes

A124941 on the OEIS · family multiplicative

Weight–level plate of Numbers k such that k and k+4 are 4-almost primes
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 viewerA124941 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L26,200 · 26.20 %
Weight class, k ≤ L73,797 · 73.80 %
Ties, k = L8
On the level line L = 13,773
Forced level, l ≤ d²69
Range of a(n)36 … 2,830,430
Range of the jump d1 … 306
Largest weight k, level L2,829,887, 1,414,550

256 different gaps occur, from 1 to 306; the level share is 26.20 %.

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.