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A031406
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 3.
1
11, 19, 23, 40, 87, 96, 152, 159, 216, 219, 235, 335, 336, 344, 392, 415, 455, 515, 535, 567, 592, 615, 688, 707, 747, 816, 848, 875, 888, 920, 927, 944, 976, 1072, 1080, 1099, 1111, 1143, 1183, 1199, 1200, 1211, 1243, 1320, 1328, 1359, 1360, 1456, 1507, 1547
OFFSET
1,1
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]] == 3, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)
cf3Q[n_]:=Module[{s=Sqrt[n], cf, len}, cf=If[IntegerQ[s], {1}, ContinuedFraction[ s][[2]]]; len=Length[cf]; EvenQ[len]&&cf[[len/2]] == 3]; Select[Range[1600], cf3Q] (* Harvey P. Dale, Aug 15 2015 *)
CROSSREFS
KEYWORD
nonn
STATUS
approved