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A031404
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 1.
20
3, 7, 8, 15, 24, 32, 35, 48, 63, 75, 80, 88, 91, 99, 115, 120, 135, 136, 143, 168, 175, 176, 195, 208, 215, 224, 247, 255, 279, 280, 288, 304, 312, 319, 323, 360, 399, 403, 427, 432, 440, 464, 483, 528, 539, 551, 555, 560, 575, 595, 611, 624, 671, 675, 696
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]] == 1, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014 *)
CROSSREFS
KEYWORD
nonn
EXTENSIONS
Names of A031404-A031423 clarified by N. J. A. Sloane, Aug 18 2021
STATUS
approved