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A031420 Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified September 28 12:34 EDT 2020. Contains 337393 sequences. (Running on oeis4.)