A232532 Positive numbers not of the form x^2 - 3*y^2; complement of A084916.

2, 3, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 19, 20, 21, 23, 26, 27, 28, 29, 30, 31, 32, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 50, 51, 53, 55, 56, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 95, 98, 99

Offset: 1

Author

V. Raman, Nov 25 2013

Keywords

• nonn

Comments

Previous name was: Numbers j such that the equation a^2 + 3*j*b^2 = 3*c^2 + j*d^2 has no solutions in positive integers for a, b, c, d.

If j is in the sequence, so is j*k^2 for any positive integer k. - Charles R Greathouse IV, Dec 13 2013

Links

• V. Raman, Proof for individual terms

Crossrefs

Cf. A084916 (complement).

Cf. A232531, A232681, A232682.

Programs

PARI

for(n=1,99, if ([]==qfbsolve(Qfb(1,0,-3),n,2),print1(n,", "))); \\ Joerg Arndt, Jun 05 2022

Extensions

Six more terms from V. Raman, Dec 13 2013

Edited by and better name from Jon E. Schoenfield and Joerg Arndt, Jun 05 2022