decompwlj 3D

Primes p such that q-p = 46, where q is the next prime after p

A134122 on the OEIS · family primes

Weight–level plate of Primes p such that q-p = 46, 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 viewerA134122 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L65,352 · 65.35 %
Weight class, k ≤ L34,648 · 34.65 %
Ties, k = L8
On the level line L = 114,908
Forced level, l ≤ d²5,881
Range of a(n)81,463 … 315,784,471
Range of the jump d48 … 37,254
Largest weight k, level L315,749,299, 5,109,133

2,986 different gaps occur, from 48 to 37,254; the level share is 65.35 %; 5.9 % 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.