decompwlj 3D

Primes of the form 7x^2 + 10y^2

A107178 on the OEIS · family quadratic form

Weight–level plate of Primes of the form 7x^2 + 10y^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 viewerA107178 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L37,684 · 37.69 %
Weight class, k ≤ L62,312 · 62.31 %
Ties, k = L7
On the level line L = 15,778
Forced level, l ≤ d²156
Range of a(n)7 … 12,183,673
Range of the jump d6 … 1,150
Largest weight k, level L12,182,843, 1,739,933

194 different gaps occur, from 6 to 1,150; the level share is 37.69 %.

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.