A332245 - OEIS

A332245

Positive integers represented by the ternary quadratic form 5x^2 + 8y^2 + 8z^2 - 5yz - xz - 4xy; equally, positive integers represented by the ternary quadratic form 5x^2 + 5y^2 + 8z^2 - yz - 4xz - 2xy.

%I #9 Feb 10 2020 20:29:48

%S 5,8,9,11,12,14,17,20,21,23,26,29,30,32,35,36,38,39,41,44,45,47,48,50,

%T 53,56,57,59,62,63,65,66,68,71,72,74,75,77,80,81,83,84,86,89,90,92,93,

%U 95,98,99,101,102,104,107,108,110,111,113,116,117,119,120,122

%N Positive integers represented by the ternary quadratic form 5x^2 + 8y^2 + 8z^2 - 5yz - xz - 4xy; equally, positive integers represented by the ternary quadratic form 5x^2 + 5y^2 + 8z^2 - yz - 4xz - 2xy.

%C Ju shows that the integers represented by the two ternary forms are identical.

%C This is S1 on Table 1.1 of Ju's paper.

%H Charles R Greathouse IV, <a href="/A332245/b332245.txt">Table of n, a(n) for n = 1..10000</a>

%H Jangwon Ju, <a href="https://arxiv.org/abs/2002.02205">Ternary quadratic forms representing same integers</a>, arXiv:2002.02205 [math.NT], 2020.

%H <a href="/index/Qua#quadform">Index entries for sequences related to quadratic forms</a>

%e 9 is (1, 1, 0) in the first form since 9 = 5*1^2 + 8*1^2 - 4*1*1 = 5 + 8 - 4. It is (1, 0, 1) in the second form for similar reasons.

%e 14 is (-1, 0, 1) in the first form since 14 = 5*(-1)^2 + 8*1^2 - (-1)*1 = 5 + 8 + 1. It is (0, -1, 1) in the second form since 14 = 5*(-1)^2 + 8*1^2 - (-1)*1 = 5 + 8 + 1.

%Y Cf. A317965.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Feb 08 2020