decompwlj 3D

Primes of the form 159587584529 + 2*n^2

A271819 on the OEIS · family primes

Weight–level plate of Primes of the form 159587584529 + 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 viewerA271819 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L96,994 · 96.99 %
Weight class, k ≤ L3,006 · 3.01 %
Ties, k = L0
On the level line L = 16,279
Forced level, l ≤ d²88,320
Range of a(n)159,587,584,529 … 499,679,020,441
Range of the jump d2 … 61,580,142
Largest weight k, level L499,669,123,693, 53,195,861,509

98,932 different gaps occur, from 2 to 61,580,142; the level share is 96.99 %; 88.3 % 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.