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 A079896 Discriminants of indefinite binary quadratic forms. 33
 5, 8, 12, 13, 17, 20, 21, 24, 28, 29, 32, 33, 37, 40, 41, 44, 45, 48, 52, 53, 56, 57, 60, 61, 65, 68, 69, 72, 73, 76, 77, 80, 84, 85, 88, 89, 92, 93, 96, 97, 101, 104, 105, 108, 109, 112, 113, 116, 117, 120, 124, 125, 128, 129, 132, 133, 136, 137, 140, 141, 145, 148 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Numbers n such that n == 0 (mod 4) or n == 1 (mod 4), but n is not a square. 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. Also, a superset of A227453. - Ralf Stephan, Sep 22 2013 For the period length of the continued fraction of sqrt(a(n)) see A267857(n). - Wolfdieter Lang, Feb 18 2016 REFERENCES A. Scholz and B. Schoeneberg, Einführung in die Zahlentheorie, 5. Aufl., de Gruyter, Berlin, New York, 1973, p. 112. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..2000 S. R. Finch, Class number theory Steven R. Finch, Class number theory [Cached copy, with permission of the author] FORMULA a(2*k^2 + 2*k) = 4*(k+1)^2 + 1 for k >= 0. - Gheorghe Coserea, Nov 07 2016 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 MATHEMATICA Select[ Range, (Mod[ #, 4] == 0 || Mod[ #, 4] == 1) && !IntegerQ[ Sqrt[ # ]] & ] PROG (PARI) seq(N) = {   my(n = 1, v = vector(N), top = 0);   while (top < N,     if (n%4 < 2 && !issquare(n), v[top++] = n); n++; );   return(v); }; seq(62) \\ Gheorghe Coserea, Nov 07 2016 CROSSREFS Cf. A014601, A042948 (with squares), A087048 (class numbers), A267857. Sequence in context: A076635 A294227 A116602 * A133315 A003658 A003656 Adjacent sequences:  A079893 A079894 A079895 * A079897 A079898 A079899 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jan 31 2003 EXTENSIONS More terms from Robert G. Wilson v, Mar 26 2003 STATUS approved

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Last modified September 29 17:46 EDT 2022. Contains 357090 sequences. (Running on oeis4.)