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%I #54 Mar 21 2023 02:23:52
%S 5,8,12,13,17,20,21,24,28,29,32,33,37,40,41,44,45,48,52,53,56,57,60,
%T 61,65,68,69,72,73,76,77,80,84,85,88,89,92,93,96,97,101,104,105,108,
%U 109,112,113,116,117,120,124,125,128,129,132,133,136,137,140,141,145,148
%N Discriminants of indefinite binary quadratic forms.
%C Numbers n such that n == 0 (mod 4) or n == 1 (mod 4), but n is not a square.
%C For an indefinite binary quadratic form over the integers a*x^2 + b*x*y + c*y^2 the discriminant is D = b^2 - 4*a*c > 0; and D not a square is assumed.
%C Also, a superset of A227453. - _Ralf Stephan_, Sep 22 2013
%C For the period length of the continued fraction of sqrt(a(n)) see A267857(n). - _Wolfdieter Lang_, Feb 18 2016
%C [I changed the offset to 1, since this is an important list. Many parts of the entry, including the b-file, will need to be changed. - _N. J. A. Sloane_, Mar 14 2023]
%D McMullen, Curtis. "Billiards and Teichmüller curves." Bulletin of the American Mathematical Society, 60:2 (2023), 195-250. See Table C.1.
%D A. Scholz and B. Schoeneberg, Einführung in die Zahlentheorie, 5. Aufl., de Gruyter, Berlin, New York, 1973, p. 112.
%H Vincenzo Librandi, <a href="/A079896/b079896.txt">Table of n, a(n) for n = 1..2001</a>
%H S. R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Class number theory</a>
%H Steven R. Finch, <a href="/A000924/a000924.pdf">Class number theory</a> [Cached copy, with permission of the author]
%F a(2*k^2 + 2*k) = 4*(k+1)^2 + 1 for k >= 0. - _Gheorghe Coserea_, Nov 07 2016
%F a(2*k^2 + 4*k + 1 + (k+1)*(-1)^k) = (2*k + 3)*(2*k + 3 + (-1)^k) for k >= 0. - _Bruno Berselli_, Nov 10 2016
%t Select[ Range[148], (Mod[ #, 4] == 0 || Mod[ #, 4] == 1) && !IntegerQ[ Sqrt[ # ]] & ]
%o (PARI) seq(N) = {
%o my(n = 1, v = vector(N), top = 0);
%o while (top < N,
%o if (n%4 < 2 && !issquare(n), v[top++] = n); n++;);
%o return(v);
%o };
%o seq(62) \\ _Gheorghe Coserea_, Nov 07 2016
%Y Cf. A014601, A042948 (with squares), A087048 (class numbers), A267857.
%K nonn,easy
%O 1,1
%A _Wolfdieter Lang_, Jan 31 2003
%E More terms from _Robert G. Wilson v_, Mar 26 2003
%E Offset changed to 1 (since this is a list). - _N. J. A. Sloane_, Mar 14 2023
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