decompwlj 3D

Numbers k such that 3*k^2 + 16 is prime

A111068 on the OEIS · family prime values

Weight–level plate of Numbers k such that 3*k^2 + 16 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 viewerA111068 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L30,776 · 30.78 %
Weight class, k ≤ L69,220 · 69.22 %
Ties, k = L29
On the level line L = 115,802
Forced level, l ≤ d²12
Range of a(n)1 … 1,644,009
Range of the jump d2 … 170
Largest weight k, level L1,643,989, 547,745

73 different gaps occur, from 2 to 170; the level share is 30.78 %; L = 1 holds 51 % 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.