decompwlj 3D

Primes congruent to 31 mod 43

A142280 on the OEIS · family primes

Weight–level plate of Primes congruent to 31 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 viewerA142280 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L50,335 · 50.34 %
Weight class, k ≤ L49,664 · 49.66 %
Ties, k = L4
On the level line L = 16,109
Forced level, l ≤ d²1,115
Range of a(n)31 … 71,496,389
Range of the jump d86 … 6,450
Largest weight k, level L71,479,361, 820,643

67 different gaps occur, from 86 to 6,450; the level share is 50.34 %; 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.