The On-Line Encyclopedia of Integer Sequences (OEIS)

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A106753

Discriminants, negated, of definite binary quadratic forms.
(history; published version)

#3 by Charles R Greathouse IV at Fri Oct 12 14:39:32 EDT 2012

AUTHOR

S. R. Finch (Steven.Finch(AT)inria.fr), May 16 2005

Steven Finch, May 16 2005

Discussion

Fri Oct 12

14:39

OEIS Server: https://oeis.org/edit/global/1837

#2 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

KEYWORD

easy,nonn,new

AUTHOR

Steven S. R. Finch (Steven.Finch(AT)inria.fr), May 16 2005

#1 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

NAME

Discriminants, negated, of definite binary quadratic forms.

DATA

3, 7, 8, 11, 12, 15, 19, 20, 23, 24, 27, 28, 31, 32, 35, 39, 40, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 63, 67, 68, 71, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 96, 99, 103, 104, 107, 108, 111, 112, 115, 116, 119, 120, 123, 124, 127, 128, 131, 132, 135, 136, 139

OFFSET

1,1

COMMENTS

A definite binary quadratic form a*x^2 + b*x*y + c*y^2 over the integers has discriminant D = b^2 - 4*a*c < 0; -D is assumed to be a nonsquare.

FORMULA

-a(n) is 0 (mod 4) or 1 (mod 4), but not a square.

MATHEMATICA

Select[ Range[148], (Mod[ -#, 4] == 0 || Mod[ -#, 4] == 1) && !IntegerQ[Sqrt[ # ]] & ]

CROSSREFS

Cf. A014601, A042948 (with squares), A079896 (indefinite case).

KEYWORD

easy,nonn

AUTHOR

Steven Finch (Steven.Finch(AT)inria.fr), May 16 2005

STATUS

approved