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 A175550 #21 May 27 2024 07:14:35
%S A175550 1,6,6,44,232,84,138,133,336,396,28656,3016,84,514228,335824,152214,
%T A175550 67830,4440,261744,504628,108373609,47124,3295440,2971215072,49349664,
%U A175550 45240,4438362040,203028,3599596,10841042784,104340657248,252736776688
%N A175550 Period of the decimal expansion of 1/F as F runs through the Fibonacci numbers greater than 1 and not divisible by 2 or 5.
%C A175550 The Fibonacci numbers contributing to this sequence are {3, 13, 21, 89, 233, ...}, i.e., Fibonacci(k) for k = 4, 7, 8, 11, 13, ... (A229829, starting with A229829(3)).
%e A175550 For n = 1, the 1st Fibonacci number > 1 and coprime to 2 and 5 is Fibonacci(4) = 3, and period(1/3) = 1, so a(1) = 1.
%e A175550 For n = 2, the 2nd Fibonacci number > 1 and coprime to 2 and 5 is Fibonacci(7) = 13, and period (1/13) = 6, so a(2) = 6.
%p A175550 with(combinat, fibonacci):nn:= 50:for q from 1 to nn do:n:=fibonacci(q):indic:=0:for p from 1 to n do:if irem(10^p, n) = 1 and gcd(n, 5) = 1 and indic=0 then printf(`%d, `, p):indic:=1:else fi:od:od:
%t A175550 Table[MultiplicativeOrder[10, n/Times @@ ({2, 5}^IntegerExponent[n, {2, 5}])], {n, Select[Fibonacci[Range[3, 70]], CoprimeQ[#, 10] &]}] (* _Amiram Eldar_, May 27 2024 *)
%Y A175550 Cf. A000045, A175561, A178505, A045572, A002329, A229829.
%K A175550 nonn,base
%O A175550 1,2
%A A175550 _Michel Lagneau_, Jun 26 2010
%E A175550 a(15) onwards from _Robert G. Wilson v_, Jun 29 2010