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 A059855 Quotient cycle lengths in continued fraction expansion of sqrt(n^2+4). 0

%I

%S 1,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,

%T 5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,

%U 5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2,5,2

%N Quotient cycle lengths in continued fraction expansion of sqrt(n^2+4).

%e For even numbers 2, for odds 5 is the length of cycles: n=96,97 the integer parts and cycles are: [96],[48,192]] and [97],[48, 1, 1, 48, 194] resp. Inside cycles floor(n/2),1,1 and 2n arise.

%p with(numtheory): [seq(nops(cfrac(sqrt(k^2+4), 'periodic', 'quotients')[2]), k=1..100)];

%t a[n_] := Length @ ContinuedFraction[Sqrt[n^2 + 4]][[2]]; Array[a, 100] (* _Amiram Eldar_, May 13 2020 *)

%Y Cf. A002496, A005574, A056899, A049423, A056903, A056905.

%K nonn

%O 1,2

%A _Labos Elemer_, Feb 27 2001

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Last modified October 1 00:54 EDT 2020. Contains 337440 sequences. (Running on oeis4.)