decompwlj 3D

Primes p such that 2*p^2+2*p-41 is a prime

A155772 on the OEIS · family primes

Weight–level plate of Primes p such that 2*p^2+2*p-41 is a 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 viewerA155772 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L37,453 · 37.45 %
Weight class, k ≤ L62,544 · 62.55 %
Ties, k = L13
On the level line L = 18,189
Forced level, l ≤ d²95
Range of a(n)5 … 10,823,459
Range of the jump d2 … 1,424
Largest weight k, level L10,823,251, 3,606,703

440 different gaps occur, from 2 to 1,424; the level share is 37.45 %.

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.