decompwlj 3D

Primes of the form 272259344081 + 2*n^2

A271366 on the OEIS · family primes

Weight–level plate of Primes of the form 272259344081 + 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 viewerA271366 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L95,120 · 95.12 %
Weight class, k ≤ L4,880 · 4.88 %
Ties, k = L0
On the level line L = 15,286
Forced level, l ≤ d²81,495
Range of a(n)272,259,344,081 … 541,857,589,081
Range of the jump d2 … 39,641,280
Largest weight k, level L541,816,469,449, 90,753,114,693

98,748 different gaps occur, from 2 to 39,641,280; the level share is 95.12 %; 81.5 % 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.