A031418 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 5.

73, 373, 449, 565, 610, 757, 1021, 1145, 1193, 1594, 1669, 1906, 2053, 2074, 2138, 2314, 2477, 2593, 2861, 3065, 3145, 4129, 4346, 4373, 4469, 4498, 4721, 5018, 5114, 5386, 5741, 6025, 6317, 6617, 6737, 6925, 7241, 7489, 7522, 7897, 7978, 8017, 8186, 8314

Offset

1,1

Links

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

Example

The simple continued fraction expansion of sqrt(73) = [8, 1, 1, 5, 5, 1, 1, 16, ...] of odd period 7 with a pair of central terms both equal to 5. Another example is sqrt(373) = [19, 3, 5, 5, 3, 38, ...] of odd period 5 with a pair of central terms both equal to 5. - Michael Somos, Apr 03 2014

Mathematica

opct5Q[n_]:=Module[{s=Sqrt[n], cf, len}, If[IntegerQ[s], cf={1, 1}, cf= ContinuedFraction[s][[2]]]; len=Length[cf]; OddQ[len] && cf[[Floor[len/2]]] == cf[[Ceiling[len/2]]]==5]; Select[Range[10000], opct5Q] (* Harvey P. Dale, Feb 22 2013 *)

Crossrefs

Cf. A031404-A031423.

Subsequence of A003814.

Sequence in context: A092342 A170916 A200908 * A142229 A299103 A201961

Adjacent sequences: A031415 A031416 A031417 * A031419 A031420 A031421

Keyword

nonn

Author

David W. Wilson

Extensions

Corrected and extended by Harvey P. Dale, Feb 22 2013

Status

approved