decompwlj 3D

Semiprimes k such that k+3 is also a semiprime

A123017 on the OEIS · family multiplicative

Weight–level plate of Semiprimes k such that k+3 is also a semiprime
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 viewerA123017 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L23,386 · 23.39 %
Weight class, k ≤ L76,612 · 76.61 %
Ties, k = L6
On the level line L = 14,340
Forced level, l ≤ d²36
Range of a(n)6 … 3,429,278
Range of the jump d1 … 441
Largest weight k, level L3,428,083, 1,142,959

239 different gaps occur, from 1 to 441; the level share is 23.39 %.

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.