decompwlj 3D

Primes p == +- 3 (mod 8), or, primes p such that 2 is not a square mod p

A003629 on the OEIS · family primes

Weight–level plate of Primes p == +- 3 (mod 8), or, primes p such that 2 is not a square mod p
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 viewerA003629 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L28,014 · 28.01 %
Weight class, k ≤ L71,983 · 71.99 %
Ties, k = L15
On the level line L = 17,444
Forced level, l ≤ d²23
Range of a(n)3 … 2,748,077
Range of the jump d2 … 232
Largest weight k, level L2,747,483, 916,019

82 different gaps occur, from 2 to 232; the level share is 28.01 %.

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.