decompwlj 3D

Primes p such that p + 6 is also prime. (Lesser of a pair of sexy primes.)

A023201 on the OEIS · family primes · also known as Lesser of sexy primes

Weight–level plate of Primes p such that p + 6 is also prime. (Lesser of a pair of sexy 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 viewerA023201 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L34,578 · 34.58 %
Weight class, k ≤ L65,421 · 65.42 %
Ties, k = L14
On the level line L = 17,688
Forced level, l ≤ d²77
Range of a(n)5 … 8,319,527
Range of the jump d2 … 1,044
Largest weight k, level L8,316,437, 2,772,803

p with p + 6 prime. The terms mix 1 and 5 mod 6, and the level share, 34.58 %, lies between the primes' and the twin primes'.

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.