decompwlj 3D

Primes p such that q-p = 22, where q is the next prime after p

A061779 on the OEIS · family primes

Weight–level plate of Primes p such that q-p = 22, where q is the next prime after p
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 viewerA061779 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L54,125 · 54.13 %
Weight class, k ≤ L45,874 · 45.87 %
Ties, k = L13
On the level line L = 116,774
Forced level, l ≤ d²965
Range of a(n)1,129 … 55,208,701
Range of the jump d24 … 5,826
Largest weight k, level L55,208,113, 1,844,537

660 different gaps occur, from 24 to 5,826; the level share is 54.13 %; 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.