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
Keywords
Examples
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
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
Programs
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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 *)
Extensions
Corrected and extended by Harvey P. Dale, Feb 22 2013