The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #18 May 26 2024 08:30:34
%S 1,1,1,1,6,6,16,2,44,1,232,84,60,138,133,144,336,10,420,396,28656,66,
%T 1500,3016,5616,84,514228,60,335824,152214,9900,67830,70980,7632,4440,
%U 261744,27144,30,504628,420,108373609,47124,9120,3295440,2971215072,836418
%N Period of the decimal representation of 1/Fibonacci(n).
%C With regard to A175550, where the period of 1/Fibonacci(n) is concerned with the Fibonacci numbers such that gcd(Fibonacci(n), 10) = 1 only, this sequence is complete.
%F a(n) = A007732(A000045(n)).
%e a(8) = 6 because Fibonacci(8) = 21, and 1/21 = 0. 047619 047619 047619 047619 ... => period = 6;
%e a(9) = 16 because Fibonacci(9) = 34, and 1/34 = 0.0 2941176470588235 2941176470588235 2941176470588235 ... => period = 16.
%t Table[MultiplicativeOrder[10, n/Times @@ ({2, 5}^IntegerExponent[n, {2, 5}])], {n, Fibonacci[Range[3, 50]]}] (* _Amiram Eldar_, May 26 2024 *)
%o (PARI) a(n) = my(f=fibonacci(n)); znorder(Mod(10, f/2^valuation(f, 2)/5^valuation(f, 5))); \\ _Michel Marcus_, May 26 2024
%Y Cf. A000045, A007732, A175550, A175562.
%K nonn,base
%O 3,5
%A _Michel Lagneau_, Jul 02 2010
%E a(23) onward corrected by _Sean A. Irvine_, May 26 2024