decompwlj 3D

Numbers k such that p=k^2+2 and p+2 are primes

A086381 on the OEIS · family prime values

Weight–level plate of Numbers k such that p=k^2+2 and p+2 are 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 viewerA086381 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L47,005 · 47.01 %
Weight class, k ≤ L52,990 · 52.99 %
Ties, k = L4
On the level line L = 16
Forced level, l ≤ d²924
Range of a(n)1 … 58,891,773
Range of the jump d2 … 6,942
Largest weight k, level L19,629,901, 8,300,943

732 different gaps occur, from 2 to 6,942; the level share is 47.01 %; L = 3 holds 31 % 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.