decompwlj 3D

Primes congruent to 41 mod 51

A142501 on the OEIS · family primes

Weight–level plate of Primes congruent to 41 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 viewerA142501 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L55,579 · 55.58 %
Weight class, k ≤ L44,420 · 44.42 %
Ties, k = L0
On the level line L = 115,835
Forced level, l ≤ d²794
Range of a(n)41 … 53,536,781
Range of the jump d102 … 4,692
Largest weight k, level L53,530,457, 518,915

43 different gaps occur, from 102 to 4,692; the level share is 55.58 %; 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.