decompwlj 3D

Primes congruent to 31 mod 51

A142495 on the OEIS · family primes

Weight–level plate of Primes congruent to 31 mod 51
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 viewerA142495 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L55,293 · 55.29 %
Weight class, k ≤ L44,705 · 44.71 %
Ties, k = L0
On the level line L = 115,686
Forced level, l ≤ d²790
Range of a(n)31 … 53,578,897
Range of the jump d102 … 5,508
Largest weight k, level L53,574,511, 518,395

42 different gaps occur, from 102 to 5,508; the level share is 55.29 %; 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.