decompwlj 3D

Lower prime of a pair of consecutive primes having a difference of 16

A031934 on the OEIS · family primes

Weight–level plate of Lower prime of a pair of consecutive primes having a difference of 16
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 viewerA031934 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L52,295 · 52.30 %
Weight class, k ≤ L47,705 · 47.70 %
Ties, k = L17
On the level line L = 115,802
Forced level, l ≤ d²749
Range of a(n)1,831 … 43,709,623
Range of the jump d18 … 4,920
Largest weight k, level L43,706,413, 2,259,565

538 different gaps occur, from 18 to 4,920; the level share is 52.30 %; L = 1 holds 30 % of the level class.

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.