decompwlj 3D

Primes p with prime(p) - p - 1 and prime(p) - p + 1 both prime

A236119 on the OEIS · family primes

Weight–level plate of Primes p with prime(p) - p - 1 and prime(p) - p + 1 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 viewerA236119 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,994
Level class, k > L56,982 · 56.99 %
Weight class, k ≤ L43,012 · 43.01 %
Ties, k = L1
On the level line L = 17,491
Forced level, l ≤ d²3,523
Range of a(n)5 … 185,763,089
Range of the jump d2 … 22,370
Largest weight k, level L185,748,821, 61,737,829

4,892 different gaps occur, from 2 to 22,370; the level share is 56.99 %; 3.5 % of terms are forced level (l <= d^2); 6 terms do not decompose.

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.