decompwlj 3D

Primes congruent to 9 mod 31

A142013 on the OEIS · family primes

Weight–level plate of Primes congruent to 9 mod 31
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 viewerA142013 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L48,121 · 48.12 %
Weight class, k ≤ L51,876 · 51.88 %
Ties, k = L6
On the level line L = 16,313
Forced level, l ≤ d²734
Range of a(n)71 … 49,918,937
Range of the jump d62 … 5,084
Largest weight k, level L49,909,513, 792,183

68 different gaps occur, from 62 to 5,084; the level share is 48.12 %.

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.