decompwlj 3D

Primes of form 4*n^2 + 4*n + 653

A145202 on the OEIS · family primes

Weight–level plate of Primes of form 4*n^2 + 4*n + 653
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 viewerA145202 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L99,999 · 100.00 %
Weight class, k ≤ L1 · 0.00 %
Ties, k = L0
On the level line L = 16,858
Forced level, l ≤ d²99,997
Range of a(n)653 … 557,317,493,021
Range of the jump d8 … 107,250,424
Largest weight k, level L557,081,611,781, 183,775

97,265 different gaps occur, from 8 to 107,250,424; every decomposable term is forced level (l <= d^2).

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.