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.

5, 8, 9, 11, 12, 14, 17, 20, 21, 23, 26, 29, 30, 32, 35, 36, 38, 39, 41, 44, 45, 47, 48, 50, 53, 56, 57, 59, 62, 63, 65, 66, 68, 71, 72, 74, 75, 77, 80, 81, 83, 84, 86, 89, 90, 92, 93, 95, 98, 99, 101, 102, 104, 107, 108, 110, 111, 113, 116, 117, 119, 120, 122

Offset

1,1

Comments

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

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Jangwon Ju, Ternary quadratic forms representing same integers, arXiv:2002.02205 [math.NT], 2020.

Index entries for sequences related to quadratic forms

Example

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.
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.

Crossrefs

Cf. A317965.

Sequence in context: A191977 A349887 A356252 * A101079 A066812 A100832

Adjacent sequences: A332242 A332243 A332244 * A332246 A332247 A332248

Keyword

nonn

Author

Charles R Greathouse IV, Feb 08 2020

Status

approved