decompwlj 3D

Prime numbers == 7 (mod 9)

A061241 on the OEIS · family primes

Weight–level plate of Prime numbers == 7 (mod 9)
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 viewerA061241 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L42,717 · 42.72 %
Weight class, k ≤ L57,281 · 57.28 %
Ties, k = L29
On the level line L = 116,613
Forced level, l ≤ d²97
Range of a(n)7 … 8,962,081
Range of the jump d18 … 792
Largest weight k, level L8,960,803, 471,535

44 different gaps occur, from 18 to 792; the level share is 42.72 %; L = 1 holds 39 % 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.