decompwlj 3D

Primes p such that 210*p + 1 is also prime

A051647 on the OEIS · family primes

Weight–level plate of Primes p such that 210*p + 1 is also 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 viewerA051647 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L34,310 · 34.31 %
Weight class, k ≤ L65,686 · 65.69 %
Ties, k = L14
On the level line L = 17,884
Forced level, l ≤ d²65
Range of a(n)2 … 6,931,549
Range of the jump d1 … 964
Largest weight k, level L6,930,587, 2,310,195

289 different gaps occur, from 1 to 964; the level share is 34.31 %.

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.