decompwlj 3D

Primes congruent to 9 mod 43

A142258 on the OEIS · family primes

Weight–level plate of Primes congruent to 9 mod 43
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 viewerA142258 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L50,361 · 50.36 %
Weight class, k ≤ L49,637 · 49.64 %
Ties, k = L7
On the level line L = 16,156
Forced level, l ≤ d²1,140
Range of a(n)181 … 71,392,049
Range of the jump d86 … 7,482
Largest weight k, level L71,363,927, 818,041

71 different gaps occur, from 86 to 7,482; the level share is 50.36 %; 1.1 % of terms are forced level (l <= d^2).

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.