decompwlj 3D

Primes of the form 666*k - 1

A063472 on the OEIS · family primes

Weight–level plate of Primes of the form 666*k - 1
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 viewerA063472 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L68,856 · 68.86 %
Weight class, k ≤ L31,143 · 31.14 %
Ties, k = L0
On the level line L = 113,710
Forced level, l ≤ d²7,011
Range of a(n)1,997 … 405,123,137
Range of the jump d666 … 37,962
Largest weight k, level L405,115,811, 603,395

56 different gaps occur, from 666 to 37,962; the level share is 68.86 %; 7.0 % 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.