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A206587 Numbers k such that the periodic part of the continued fraction of sqrt(k) has even length. 2
1, 3, 4, 6, 7, 8, 9, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 59, 60, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 75, 76, 77, 78, 79, 80, 81, 83, 84 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is A206586 and the squares, A000290.

LINKS

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

MATHEMATICA

Select[Range[100], IntegerQ[Sqrt[#]] || EvenQ[Length[ContinuedFraction[Sqrt[#]][[2]]]] &]

PROG

(PARI)

cyc(cf) = {

  if(#cf==1, return([])); \\ There is no cycle

  my(s=[]);

  for(k=2, #cf,

    s=concat(s, cf[k]);

    if(cf[k]==2*cf[1], return(s)) \\ Cycle found

  );

  0 \\ Cycle not found

}

select(n->#cyc(contfrac(sqrt(n)))%2==0, vector(400, n, n)) \\ Colin Barker, Oct 19 2014

CROSSREFS

Cf. A003814 (period has odd length).

Cf. A000290, A206586.

Sequence in context: A058654 A188435 A047517 * A192450 A039064 A187953

Adjacent sequences:  A206584 A206585 A206586 * A206588 A206589 A206590

KEYWORD

nonn

AUTHOR

T. D. Noe, Mar 20 2012

STATUS

approved

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Last modified December 3 20:25 EST 2021. Contains 349468 sequences. (Running on oeis4.)