A031404 - OEIS

A031404

Numbers k such that the continued fraction for sqrt(k) has even period 2*m and the m-th term of the periodic part is 1.

3, 7, 8, 15, 24, 32, 35, 48, 63, 75, 80, 88, 91, 99, 115, 120, 135, 136, 143, 168, 175, 176, 195, 208, 215, 224, 247, 255, 279, 280, 288, 304, 312, 319, 323, 360, 399, 403, 427, 432, 440, 464, 483, 528, 539, 551, 555, 560, 575, 595, 611, 624, 671, 675, 696

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OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

MATHEMATICA

n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[EvenQ[len] && c[[2, len/2]] == 1, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)

CROSSREFS

Cf. A031405-A031423.

Sequence in context: A045542 A249435 A192120 * A263519 A105263 A242572

Adjacent sequences: A031401 A031402 A031403 * A031405 A031406 A031407

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Names of A031404-A031423 clarified by N. J. A. Sloane, Aug 18 2021

STATUS

approved