decompwlj 3D

Not of the form x^2 + x*y + y^2

A034020 on the OEIS · family quadratic form

Weight–level plate of Not of the form x^2 + x*y + 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 viewerA034020 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L9,150 · 9.15 %
Weight class, k ≤ L90,849 · 90.85 %
Ties, k = L97
On the level line L = 17,825
Forced level, l ≤ d²2
Range of a(n)2 … 124,781
Range of the jump d1 … 3
Largest weight k, level L124,771, 62,390

The gaps are 1, 2 and 3; the level share is 9.15 %; L = 1 holds 86 % of the level class.

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.