decompwlj 3D

Primes followed by a larger-than-average prime gap

A082885 on the OEIS · family primes

Weight–level plate of Primes followed by a larger-than-average prime gap
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 viewerA082885 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L33,659 · 33.66 %
Weight class, k ≤ L66,338 · 66.34 %
Ties, k = L14
On the level line L = 18,934
Forced level, l ≤ d²26
Range of a(n)2 … 3,790,103
Range of the jump d1 … 218
Largest weight k, level L3,789,757, 222,315

90 different gaps occur, from 1 to 218; the level share is 33.66 %.

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.