The On-Line Encyclopedia of Integer Sequences (OEIS)

A106753 revision #3

A106753

Discriminants, negated, of definite binary quadratic forms.

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

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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.

LINKS

Table of n, a(n) for n=1..64.

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).

Sequence in context: A261415 A331547 A285164 * A174871 A062863 A194470

Adjacent sequences: A106750 A106751 A106752 * A106754 A106755 A106756

KEYWORD

easy,nonn

AUTHOR

Steven Finch, May 16 2005

STATUS

approved