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

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A031404-A031423.

Subsequence of A003814.

Programs

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 *)

Extensions

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