decompwlj 3D

Primes not congruent to -1 (mod 7)

A042988 on the OEIS · family primes

Weight–level plate of Primes not congruent to -1 (mod 7)
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 viewerA042988 on the OEIS
Terms100,000 (n = 0 … 99,999)
Decomposable (a > 2d)99,996
Level class, k > L25,731 · 25.73 %
Weight class, k ≤ L74,265 · 74.27 %
Ties, k = L7
On the level line L = 18,046
Forced level, l ≤ d²12
Range of a(n)2 … 1,583,459
Range of the jump d1 … 140
Largest weight k, level L1,583,447, 527,763

66 different gaps occur, from 1 to 140; the level share is 25.73 %; L = 1 holds 31 % 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.