decompwlj 3D

Lower prime of a difference of 8 between consecutive primes

A031926 on the OEIS · family primes

Weight–level plate of Lower prime of a difference of 8 between consecutive primes
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 viewerA031926 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L49,171 · 49.17 %
Weight class, k ≤ L50,828 · 50.83 %
Ties, k = L0
On the level line L = 116,593
Forced level, l ≤ d²330
Range of a(n)89 … 26,065,379
Range of the jump d12 … 2,988
Largest weight k, level L26,063,783, 1,980,713

342 different gaps occur, from 12 to 2,988; the level share is 49.17 %; L = 1 holds 34 % of the level class; 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.