

A031418


Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 5.


1



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
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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. A031404A031423.
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



