decompwlj 3D

Primes p such that 8*p^2 + 4*p + 1 is also prime

A103776 on the OEIS · family primes

Weight–level plate of Primes p such that 8*p^2 + 4*p + 1 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 viewerA103776 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L43,616 · 43.62 %
Weight class, k ≤ L56,378 · 56.38 %
Ties, k = L5
On the level line L = 17,723
Forced level, l ≤ d²312
Range of a(n)2 … 24,321,907
Range of the jump d4 … 3,754
Largest weight k, level L24,321,757, 3,471,399

547 different gaps occur, from 4 to 3,754; the level share is 43.62 %; 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.