decompwlj 3D

Primes of the form 16n+1

A094407 on the OEIS · family primes

Weight–level plate of Primes of the form 16n+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 viewerA094407 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L38,235 · 38.24 %
Weight class, k ≤ L61,763 · 61.76 %
Ties, k = L20
On the level line L = 16,476
Forced level, l ≤ d²145
Range of a(n)17 … 12,205,393
Range of the jump d16 … 1,344
Largest weight k, level L12,205,121, 716,865

59 different gaps occur, from 16 to 1,344; the level share is 38.24 %.

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.