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A031416 Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 3. 1
89, 149, 193, 218, 250, 277, 337, 493, 521, 569, 653, 709, 914, 1009, 1018, 1037, 1385, 1465, 1553, 1597, 1618, 1754, 1781, 1898, 1921, 1973, 1994, 2069, 2129, 2146, 2293, 2378, 2389, 2441, 2474, 2561, 2725, 2741, 2777, 2897, 2957, 2986, 3170, 3229, 3265 (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] < 60, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 3, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 03 2014 *)

cfo3Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {0, 0}, ContinuedFraction[ s ][[2]]]; len=Length[cf]; OddQ[len]&&cf[[ (len+1)/2]] == cf[[(len-1)/2]]==3]; Select[Range[3300], cfo3Q] (* Harvey P. Dale, Sep 25 2019 *)

CROSSREFS

Cf. A031404-A031423.

Sequence in context: A260557 A141938 A267819 * A247114 A075589 A142031

Adjacent sequences:  A031413 A031414 A031415 * A031417 A031418 A031419

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Initial 10 removed by T. D. Noe, Apr 03 2014

STATUS

approved

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Last modified September 24 04:19 EDT 2020. Contains 337317 sequences. (Running on oeis4.)