decompwlj 3D

a(n) and a(n)+64 both prime

A049490 on the OEIS · family primes

Weight–level plate of a(n) and a(n)+64 both prime
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 viewerA049490 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L47,280 · 47.28 %
Weight class, k ≤ L52,716 · 52.72 %
Ties, k = L40
On the level line L = 117,570
Forced level, l ≤ d²190
Range of a(n)3 … 18,496,129
Range of the jump d4 … 1,950
Largest weight k, level L18,495,877, 1,676,111

248 different gaps occur, from 4 to 1,950; the level share is 47.28 %; L = 1 holds 37 % 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.