decompwlj 3D

Primes of the form 236241327599 + 2*n^2

A271820 on the OEIS · family primes

Weight–level plate of Primes of the form 236241327599 + 2*n^2
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 viewerA271820 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L96,572 · 96.57 %
Weight class, k ≤ L3,428 · 3.43 %
Ties, k = L0
On the level line L = 15,838
Forced level, l ≤ d²85,902
Range of a(n)236,241,327,599 … 578,384,482,927
Range of the jump d2 … 75,966,792
Largest weight k, level L578,308,383,271, 78,747,109,199

98,835 different gaps occur, from 2 to 75,966,792; the level share is 96.57 %; 85.9 % of terms are forced level (l <= d^2); there are no ties.

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.