decompwlj 3D

Primes congruent to 1 mod 31

A142005 on the OEIS · family primes

Weight–level plate of Primes congruent to 1 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 viewerA142005 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L48,221 · 48.22 %
Weight class, k ≤ L51,777 · 51.78 %
Ties, k = L3
On the level line L = 16,258
Forced level, l ≤ d²763
Range of a(n)311 … 50,080,253
Range of the jump d62 … 4,898
Largest weight k, level L50,062,769, 794,469

65 different gaps occur, from 62 to 4,898; the level share is 48.22 %.

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.