decompwlj 3D

Primes of the form 666*n + 1

A037029 on the OEIS · family primes

Weight–level plate of Primes of the form 666*n + 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 viewerA037029 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L69,070 · 69.07 %
Weight class, k ≤ L30,929 · 30.93 %
Ties, k = L8
On the level line L = 113,522
Forced level, l ≤ d²6,952
Range of a(n)1,999 … 405,384,211
Range of the jump d666 … 35,964
Largest weight k, level L405,339,589, 581,951

52 different gaps occur, from 666 to 35,964; the level share is 69.07 %; 7.0 % of terms are forced level (l <= d^2).

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.