decompwlj 3D

Numbers k such that 8*k^2+1 is a prime

A188549 on the OEIS · family prime values

Weight–level plate of Numbers k such that 8*k^2+1 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 viewerA188549 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L19,679 · 19.68 %
Weight class, k ≤ L80,319 · 80.32 %
Ties, k = L3
On the level line L = 12
Forced level, l ≤ d²20
Range of a(n)3 … 2,038,767
Range of the jump d3 … 216
Largest weight k, level L679,537, 509,676

62 different gaps occur, from 3 to 216; the level share is 19.68 %; L = 3 holds 41 % 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.