decompwlj 3D

Primes congruent to 1 or 19 (mod 30)

A033212 on the OEIS · family primes

Weight–level plate of Primes congruent to 1 or 19 (mod 30)
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 viewerA033212 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L43,833 · 43.83 %
Weight class, k ≤ L56,165 · 56.17 %
Ties, k = L43
On the level line L = 123,555
Forced level, l ≤ d²59
Range of a(n)19 … 5,807,539
Range of the jump d12 … 660
Largest weight k, level L5,807,029, 446,419

46 different gaps occur, from 12 to 660; the level share is 43.83 %; L = 1 holds 54 % of the level class.

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.