%I A059853
%S A059853 4,2,6,4,2,6,10,2,12,16,2,16,20,2,10,10,2,12,10,2,28,10,2,26,16,2,18,
%T A059853 48,2,34,12,2,26,32,2,32,32,2,20,70,2,56,34,2,24,22,2,54,52,2,70,16,2,
%U A059853 18,38,2,16,36,2,12,72,2,114,30,2,64,32,2,52,54,2,22,92,2,154,88,2,56
%N A059853 Quotient cycle length of Sqrt(n^2+3).
%e A059853 If n=3k than a(n)=2, otherwise changing. Integer parts and cycles for 
               n=35, 36 and 37 are (with lengths=32, 2, 32): [[35], [23, 2, 1, 7, 
               8, 1, 1, 1, 2, 2, 1, 1, 5, 3, 1, 16, 1, 3, 5, 1, 1, 2, 2, 1, 1, 1, 
               8, 7, 1, 2, 23, 70]], [[36], [24, 72]] or [[37], [24, 1, 2, 7, 1, 
               8, 2, 1, 1, 1, 2, 2, 5, 1, 3, 18, 3, 1, 5, 2, 2, 1, 1, 1, 2, 8, 1, 
               7, 2, 1, 24, 74]].
%p A059853 with(numtheory): [seq(nops(cfrac(sqrt(k^2+3),'periodic','quotients')[2]),
               k=2..256)];
%Y A059853 A002496, A005575, A056899, A049423, A056903.
%Y A059853 Sequence in context: A129131 A097467 A092205 this_sequence A136527 A138614 
               A161912
%Y A059853 Adjacent sequences: A059850 A059851 A059852 this_sequence A059854 A059855 
               A059856
%K A059853 nonn
%O A059853 2,1
%A A059853 Labos E. (labos(AT)ana.sote.hu), Feb 27 2001