decompwlj 3D

Primes congruent to 30 mod 41

A142227 on the OEIS · family primes

Weight–level plate of Primes congruent to 30 mod 41
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 viewerA142227 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L50,128 · 50.13 %
Weight class, k ≤ L49,868 · 49.87 %
Ties, k = L0
On the level line L = 16,109
Forced level, l ≤ d²1,014
Range of a(n)71 … 67,909,847
Range of the jump d82 … 6,150
Largest weight k, level L67,873,439, 789,957

67 different gaps occur, from 82 to 6,150; the level share is 50.13 %; 1.0 % of terms are forced level (l <= d^2); 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.