|
|
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.
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Initial erroneous term 50 removed by T. D. Noe, Apr 04 2014
|
|
STATUS
|
approved
|
|
|
|