decompwlj 3D

Primes p such that q-p = 26, where q is the next prime after p

A124594 on the OEIS · family primes

Weight–level plate of Primes p such that q-p = 26, 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 viewerA124594 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L56,780 · 56.78 %
Weight class, k ≤ L43,218 · 43.22 %
Ties, k = L0
On the level line L = 116,312
Forced level, l ≤ d²1,557
Range of a(n)2,477 … 83,402,987
Range of the jump d30 … 9,180
Largest weight k, level L83,397,803, 2,355,233

960 different gaps occur, from 30 to 9,180; the level share is 56.78 %; 1.6 % of terms are forced level (l <= d^2); there are no ties.

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.