decompwlj 3D

Primes congruent to {1, 2, 3, 5} mod 19

A215309 on the OEIS · family primes

Weight–level plate of Primes congruent to {1, 2, 3, 5} mod 19
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 viewerA215309 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L33,926 · 33.93 %
Weight class, k ≤ L66,070 · 66.07 %
Ties, k = L18
On the level line L = 17,379
Forced level, l ≤ d²70
Range of a(n)2 … 6,573,793
Range of the jump d1 … 646
Largest weight k, level L6,572,711, 2,191,219

121 different gaps occur, from 1 to 646; the level share is 33.93 %.

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.