A031601 - OEIS

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A031601

Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted the two central terms are both 13.

409, 1181, 2258, 3562, 3802, 3925, 5305, 5897, 8269, 9829, 10834, 11041, 12389, 15737, 16745, 17785, 21757, 23029, 23633, 24554, 25178, 26869, 27194, 27521, 28181, 28514, 28849, 30554, 30901, 32413, 33853, 36073, 36185, 40841, 41362, 41765, 42170

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..150

MATHEMATICA

cf13Q[n_]:=Module[{per=ContinuedFraction[Sqrt[n]][[2]]}, OddQ[Length[ per]]&&per[[Floor[Length[per]/2]+1]]==13]; nn=43000; With[{terms = Complement[Range[nn], Range[Floor[Sqrt[nn]]]^2]}, Select[terms, cf13Q]] (* Harvey P. Dale, Nov 23 2011 *)

CROSSREFS

Subsequence of A003814.

Sequence in context: A321151 A052376 A201483 * A107625 A061333 A262636

Adjacent sequences: A031598 A031599 A031600 * A031602 A031603 A031604

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Corrected by Harvey P. Dale, Nov 23 2011

STATUS

approved