decompwlj 3D

Primes congruent to {1, 6} mod 7

A045472 on the OEIS · family primes

Weight–level plate of Primes congruent to {1, 6} 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 viewerA045472 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L33,747 · 33.75 %
Weight class, k ≤ L66,251 · 66.25 %
Ties, k = L10
On the level line L = 19,291
Forced level, l ≤ d²43
Range of a(n)13 … 4,255,609
Range of the jump d2 … 436
Largest weight k, level L4,255,549, 1,418,185

75 different gaps occur, from 2 to 436; the level share is 33.75 %.

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.