decompwlj 3D

Numbers n such that n + 3 and n - 3 are both prime

A087695 on the OEIS · family prime values

Weight–level plate of Numbers n such that n + 3 and n - 3 are both prime
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 viewerA087695 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L30,017 · 30.02 %
Weight class, k ≤ L69,983 · 69.98 %
Ties, k = L2
On the level line L = 11
Forced level, l ≤ d²76
Range of a(n)8 … 8,319,530
Range of the jump d2 … 1,044
Largest weight k, level L4,159,523, 2,772,804

351 different gaps occur, from 2 to 1,044; the level share is 30.02 %.

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.