decompwlj 3D

Primes p such that 2*p^2 + 2*p - 9 is prime

A308269 on the OEIS · family primes

Weight–level plate of Primes p such that 2*p^2 + 2*p - 9 is 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 viewerA308269 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L51,737 · 51.74 %
Weight class, k ≤ L48,257 · 48.26 %
Ties, k = L21
On the level line L = 115,721
Forced level, l ≤ d²558
Range of a(n)2 … 41,158,867
Range of the jump d5 … 4,338
Largest weight k, level L41,157,031, 3,161,155

334 different gaps occur, from 5 to 4,338; the level share is 51.74 %; L = 1 holds 30 % of the level class; 6 terms do not decompose.

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.