decompwlj 3D

Primes p such that 2p+3*5*7*11*13*17*19*23*29*31*37 is prime

A161613 on the OEIS · family primes

Weight–level plate of Primes p such that 2p+3*5*7*11*13*17*19*23*29*31*37 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 viewerA161613 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L34,222 · 34.22 %
Weight class, k ≤ L65,777 · 65.78 %
Ties, k = L6
On the level line L = 18,235
Forced level, l ≤ d²93
Range of a(n)41 … 6,331,789
Range of the jump d2 … 768
Largest weight k, level L6,330,719, 2,109,543

261 different gaps occur, from 2 to 768; the level share is 34.22 %.

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.