decompwlj 3D

Primes congruent to 8 mod 13

A092178 on the OEIS · family primes

Weight–level plate of Primes congruent to 8 mod 13
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 viewerA092178 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L42,691 · 42.69 %
Weight class, k ≤ L57,306 · 57.31 %
Ties, k = L0
On the level line L = 16,882
Forced level, l ≤ d²235
Range of a(n)47 … 18,808,837
Range of the jump d26 … 1,768
Largest weight k, level L18,804,521, 696,431

62 different gaps occur, from 26 to 1,768; the level share is 42.69 %; 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.