This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A175561 #18 May 26 2024 08:30:34
%S A175561 1,1,1,1,6,6,16,2,44,1,232,84,60,138,133,144,336,10,420,396,28656,66,
%T A175561 1500,3016,5616,84,514228,60,335824,152214,9900,67830,70980,7632,4440,
%U A175561 261744,27144,30,504628,420,108373609,47124,9120,3295440,2971215072,836418
%N A175561 Period of the decimal representation of 1/Fibonacci(n).
%C A175561 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 A175561 a(n) = A007732(A000045(n)).
%e A175561 a(8) = 6 because Fibonacci(8) = 21, and 1/21 = 0. 047619 047619 047619 047619 ... => period = 6;
%e A175561 a(9) = 16 because Fibonacci(9) = 34, and 1/34 = 0.0 2941176470588235 2941176470588235 2941176470588235 ... => period = 16.
%t A175561 Table[MultiplicativeOrder[10, n/Times @@ ({2, 5}^IntegerExponent[n, {2, 5}])], {n, Fibonacci[Range[3, 50]]}] (* _Amiram Eldar_, May 26 2024 *)
%o A175561 (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 A175561 Cf. A000045, A007732, A175550, A175562.
%K A175561 nonn,base
%O A175561 3,5
%A A175561 _Michel Lagneau_, Jul 02 2010
%E A175561 a(23) onward corrected by _Sean A. Irvine_, May 26 2024