decompwlj 3D

Primes p such that 8p^2 - 7p + 2 is also prime

A280273 on the OEIS · family primes

Weight–level plate of Primes p such that 8p^2 - 7p + 2 is also 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 viewerA280273 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L50,102 · 50.10 %
Weight class, k ≤ L49,893 · 49.90 %
Ties, k = L0
On the level line L = 116,674
Forced level, l ≤ d²428
Range of a(n)3 … 32,116,193
Range of the jump d2 … 3,702
Largest weight k, level L32,115,773, 4,532,111

424 different gaps occur, from 2 to 3,702; the level share is 50.10 %; L = 1 holds 33 % of the level class; there are no ties.

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.