decompwlj 3D

Primes p such that (p+1)/2 is prime

A005383 on the OEIS · family primes · also known as Primes p with (p + 1)/2 prime

Weight–level plate of Primes p such that (p+1)/2 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 viewerA005383 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,995
Level class, k > L52,158 · 52.16 %
Weight class, k ≤ L47,837 · 47.84 %
Ties, k = L34
On the level line L = 116,359
Forced level, l ≤ d²493
Range of a(n)3 … 38,695,273
Range of the jump d2 … 4,860
Largest weight k, level L38,681,233, 2,255,717

Primes p with (p + 1)/2 prime. The level share is 52.16 %; L = 1 holds 31 % 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.