login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Positive numbers not of the form x^2 - 3*y^2; complement of A084916.
4

%I #51 Jun 06 2022 08:17:23

%S 2,3,5,7,8,10,11,12,14,15,17,18,19,20,21,23,26,27,28,29,30,31,32,34,

%T 35,38,39,40,41,42,43,44,45,47,48,50,51,53,55,56,57,58,59,60,62,63,65,

%U 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

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

%C 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.

%C If j is in the sequence, so is j*k^2 for any positive integer k. - _Charles R Greathouse IV_, Dec 13 2013

%H V. Raman, <a href="/A232532/a232532.txt">Proof for individual terms</a>

%o (PARI) for(n=1,99, if ([]==qfbsolve(Qfb(1,0,-3),n,2),print1(n,", "))); \\ _Joerg Arndt_, Jun 05 2022

%Y Cf. A084916 (complement).

%Y Cf. A232531, A232681, A232682.

%K nonn

%O 1,1

%A _V. Raman_, Nov 25 2013

%E Six more terms from _V. Raman_, Dec 13 2013

%E Edited by and better name from _Jon E. Schoenfield_ and _Joerg Arndt_, Jun 05 2022