decompwlj 3D

Nonprimes of the form 6k + 1

A091300 on the OEIS · family complement

Weight–level plate of Nonprimes of the form 6k + 1
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 viewerA091300 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L32,386 · 32.39 %
Weight class, k ≤ L67,611 · 67.61 %
Ties, k = L141
On the level line L = 125,364
Forced level, l ≤ d²11
Range of a(n)1 … 789,043
Range of the jump d6 … 30
Largest weight k, level L789,031, 112,711

5 different gaps occur, from 6 to 30; the level share is 32.39 %; L = 1 holds 78 % 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.