decompwlj 3D

Primes of the form x^2 + 18480*y^2

A173274 on the OEIS · family quadratic form

Weight–level plate of Primes of the form x^2 + 18480*y^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 viewerA173274 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L68,475 · 68.47 %
Weight class, k ≤ L31,525 · 31.52 %
Ties, k = L28
On the level line L = 116,084
Forced level, l ≤ d²6,828
Range of a(n)18,481 … 361,091,641
Range of the jump d48 … 36,960
Largest weight k, level L361,038,697, 5,892,133

638 different gaps occur, from 48 to 36,960; the level share is 68.47 %; 6.8 % of terms are 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.