decompwlj 3D

Primes p such that 1 + 4p + 12p^2 is prime

A122482 on the OEIS · family primes

Weight–level plate of Primes p such that 1 + 4p + 12p^2 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 viewerA122482 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L48,954 · 48.96 %
Weight class, k ≤ L51,042 · 51.04 %
Ties, k = L29
On the level line L = 116,251
Forced level, l ≤ d²364
Range of a(n)7 … 26,866,387
Range of the jump d6 … 3,480
Largest weight k, level L26,865,409, 3,834,271

368 different gaps occur, from 6 to 3,480; the level share is 48.96 %; L = 1 holds 33 % 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.