decompwlj 3D

Primes p such that q-p = 42, where q is the next prime after p

A134120 on the OEIS · family primes

Weight–level plate of Primes p such that q-p = 42, 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 viewerA134120 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L53,169 · 53.17 %
Weight class, k ≤ L46,830 · 46.83 %
Ties, k = L3
On the level line L = 17,806
Forced level, l ≤ d²2,192
Range of a(n)16,141 … 114,619,259
Range of the jump d42 … 18,840
Largest weight k, level L114,587,867, 2,631,919

3,125 different gaps occur, from 42 to 18,840; the level share is 53.17 %; 2.2 % of terms are forced level (l <= d^2).

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.