decompwlj 3D

Primes congruent to 1 (mod 30)

A132230 on the OEIS · family primes

Weight–level plate of Primes congruent to 1 (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 viewerA132230 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L48,348 · 48.35 %
Weight class, k ≤ L51,650 · 51.65 %
Ties, k = L74
On the level line L = 122,307
Forced level, l ≤ d²140
Range of a(n)31 … 12,206,851
Range of the jump d30 … 1,050
Largest weight k, level L12,205,321, 392,461

35 different gaps occur, from 30 to 1,050; the level share is 48.35 %; L = 1 holds 46 % 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.