A031420 - OEIS

A031420

Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 7.

349, 778, 1105, 1237, 1306, 1565, 1721, 2473, 3361, 3706, 3889, 4133, 4985, 5261, 5545, 6217, 6841, 6929, 7165, 7253, 7418, 7754, 8021, 8273, 8369, 8629, 9089, 9274, 9461, 10034, 10229, 10333, 10729, 11245, 11657, 12077, 12842, 12941, 13385, 13730, 14314

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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[OddQ[len] && c[[2, (len + 1)/2]] == 7, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)

cf7Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {0}, ContinuedFraction[ s] [[2]]]; len=Length[cf]; OddQ[len]&&Count[Take[cf, {(len+1)/2-1, (len+1)/2+1}], 7]>1]; Select[Range[15000], cf7Q]//Quiet (* Harvey P. Dale, Sep 14 2016 *)

CROSSREFS

Cf. A031404-A031423.

Subsequence of A003814.

Sequence in context: A139658 A181987 A054824 * A273530 A282341 A285463

Adjacent sequences: A031417 A031418 A031419 * A031421 A031422 A031423

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Initial erroneous term 50 removed by T. D. Noe, Apr 04 2014

STATUS

approved