A010333 - OEIS

A010333

Length of period of continued for sqrt(A003814(n)).

1, 1, 1, 5, 1, 1, 5, 1, 3, 1, 5, 7, 11, 1, 7, 5, 1, 5, 5, 11, 1, 9, 15, 9, 1, 5, 3, 9, 1, 9, 17, 1, 5, 21, 5, 13, 1, 7, 5, 1, 5, 11, 17, 7, 1, 9, 3, 7, 21, 13, 1, 5, 11, 17, 7, 11, 1, 19, 5, 5, 7, 15, 1, 5, 3, 5, 9, 21, 21, 1, 21, 37, 7, 21, 1, 5, 17, 25, 3, 15, 13, 1, 9, 19, 19, 1, 5, 7, 39

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OFFSET

1,4

COMMENTS

If the period length of the continued fraction of a quadratic surd sqrt(D) is odd, the negative Pell equation x^2 - D y^2 = -1 has (infinite) solutions.

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

MATHEMATICA

Select[Map[Length@ Last@ ContinuedFraction@ Sqrt@ # &, Range[550]], OddQ] (* Michael De Vlieger, Dec 06 2017, after T. D. Noe at A003814 *)

CROSSREFS

Cf. A003814.

Sequence in context: A332762 A108691 A378962 * A378898 A131777 A323388

Adjacent sequences: A010330 A010331 A010332 * A010334 A010335 A010336

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Walter Gilbert

STATUS

approved