decompwlj 3D

Primes congruent to 1 (mod 12)

A068228 on the OEIS · family primes

Weight–level plate of Primes congruent to 1 (mod 12)
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 viewerA068228 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L40,174 · 40.17 %
Weight class, k ≤ L59,824 · 59.83 %
Ties, k = L81
On the level line L = 117,055
Forced level, l ≤ d²55
Range of a(n)13 … 5,806,657
Range of the jump d12 … 576
Largest weight k, level L5,806,441, 446,305

40 different gaps occur, from 12 to 576; the level share is 40.17 %; L = 1 holds 42 % 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.