decompwlj 3D

Primes congruent to 23 mod 45

A142324 on the OEIS · family primes

Weight–level plate of Primes congruent to 23 mod 45
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 viewerA142324 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L55,353 · 55.35 %
Weight class, k ≤ L44,645 · 44.65 %
Ties, k = L0
On the level line L = 120,739
Forced level, l ≤ d²554
Range of a(n)23 … 39,445,673
Range of the jump d90 … 3,600
Largest weight k, level L39,445,493, 433,193

38 different gaps occur, from 90 to 3,600; the level share is 55.35 %; L = 1 holds 37 % 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.