%I A066853
%S A066853 1,2,3,4,5,6,7,6,9,10,7,11,9,14,15,11,13,11,12,20,9,14,19,13,25,18,27,
%T A066853 21,10,30,19,21,19,13,35,15,29,13,25,30,19,18,33,20,45,21,15,15,37,50,
%U A066853 35,30,37,29,12,25,33,20,37,55,25,21,23,42,45,38,51,20,29,70,44,15,57
%N A066853 Number of different remainders (or residues) for the Fibonacci numbers 
               (A000045) when divided by n (i.e. the size of the set of F(i) mod 
               n over all i).
%C A066853 The Fibonacci numbers mod n for any n are periodic - see A001175 for 
               period lengths. - Ron Knott (ron(AT)ronknott.com), Jan 05 2005
%e A066853 a(8)=6 since the Fibonacci numbers, 0,1,1,2,3,5,8,13,21,34,55,89,144,
               .. when divided by 8 have remainders 0,1,1,2,3,5,0,5,5,2,7,1 (repeatedly) 
               which only contains the remainders 0,1,2,3,5 and 7, i.e. 6 remainders, 
               so a(8)=6
%e A066853 a(11)=7 since Fibonacci numbers reduced modulo 11 are {0, 1, 2, 3, 5, 
               8, 10}.
%Y A066853 Cf. A001175, A079002.
%Y A066853 Sequence in context: A005599 A071934 A161658 this_sequence A141258 A117656 
               A101918
%Y A066853 Adjacent sequences: A066850 A066851 A066852 this_sequence A066854 A066855 
               A066856
%K A066853 nonn
%O A066853 1,2
%A A066853 Reiner Martin (reinermartin(AT)hotmail.com), Jan 21 2002