decompwlj 3D

Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is prime

A158714 on the OEIS · family primes

Weight–level plate of Primes p such that p1 = ceiling(p/2) + p is prime and p2 = floor(p1/2) + p1 is 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 viewerA158714 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L65,797 · 65.80 %
Weight class, k ≤ L34,200 · 34.20 %
Ties, k = L0
On the level line L = 17,380
Forced level, l ≤ d²10,008
Range of a(n)3 … 504,245,827
Range of the jump d8 … 64,408
Largest weight k, level L504,086,867, 54,912,779

2,312 different gaps occur, from 8 to 64,408; the level share is 65.80 %; 10.0 % 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.