decompwlj 3D

Primes congruent to 23 (mod 30)

A132235 on the OEIS · family primes

Weight–level plate of Primes congruent to 23 (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 viewerA132235 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L48,365 · 48.37 %
Weight class, k ≤ L51,632 · 51.63 %
Ties, k = L0
On the level line L = 122,164
Forced level, l ≤ d²157
Range of a(n)23 … 12,187,613
Range of the jump d30 … 1,200
Largest weight k, level L12,187,313, 392,843

34 different gaps occur, from 30 to 1,200; the level share is 48.37 %; L = 1 holds 46 % of the level class; 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.