decompwlj 3D

Numbers n such that 64n+33 is prime

A105136 on the OEIS · family prime values

Weight–level plate of Numbers n such that 64n+33 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 viewerA105136 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L17,301 · 17.30 %
Weight class, k ≤ L82,697 · 82.70 %
Ties, k = L14
On the level line L = 15,359
Forced level, l ≤ d²10
Range of a(n)1 … 836,386
Range of the jump d1 … 76
Largest weight k, level L836,267, 418,059

69 different gaps occur, from 1 to 76; the level share is 17.30 %; L = 1 holds 31 % 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.