decompwlj 3D

p, p+2 and p+8 are primes

A046134 on the OEIS · family primes

Weight–level plate of p, p+2 and p+8 are 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 viewerA046134 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L65,927 · 65.93 %
Weight class, k ≤ L34,068 · 34.07 %
Ties, k = L0
On the level line L = 119,290
Forced level, l ≤ d²3,800
Range of a(n)3 … 203,892,389
Range of the jump d2 … 30,600
Largest weight k, level L203,875,691, 10,846,231

1,373 different gaps occur, from 2 to 30,600; the level share is 65.93 %; 3.8 % of terms are forced level (l <= d^2); 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.