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 A233286 #25 Jan 18 2025 09:07:00
%S A233286 0,0,1,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,1,0,
%T A233286 0,3,0,0,1,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,1,0,0,5,0,0,1,0,0,1,0,0,
%U A233286 1,0,0,3,0,0,1,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,1,0,0,3,0,0,1,0,0,1,0,0,1
%N A233286 Number of trailing zeros in the factorial base representation of n-th Fibonacci number.
%C A233286 A233285 is the main entry for this topic, see comments there.
%H A233286 Antti Karttunen, <a href="/A233286/b233286.txt">Table of n, a(n) for n = 1..100000</a>
%H A233286 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%F A233286 a(n) = A230403(A000045(n)) = A233285(n)-1.
%e A233286 The factorial base representation (A007623(A000045(n))) of Fibonacci numbers look like this, from n=1 onward: 1, 1, 10, 11, 21, 110, 201, 311, 1120, 2101, 3221, 11000, 14221, 30221, 50120, 121011, 211201, 332220, ...
%e A233286 When we count the trailing zeros of each, we get 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 1, ..., the first terms of this sequence.
%t A233286 a[n_] := Module[{k = Fibonacci[n], m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; FirstPosition[s, _?(# > 0&)][[1]] - 1]; Array[a, 100] (* _Amiram Eldar_, Feb 21 2024 *)
%o A233286 (PARI) A233286(n) = if(n<=2, 0, my(f=fibonacci(n)); for(k=2,oo,if(f%(k!), return(k-2)))); \\ _Antti Karttunen_, Jan 18 2025
%o A233286 (Scheme) (define (A233286 n) (A230403 (A000045 n)))
%Y A233286 One less than A233285. Cf. also A007623, A000045, A230403.
%K A233286 nonn,base
%O A233286 1,12
%A A233286 _Antti Karttunen_, Dec 07 2013
%E A233286 Data section extended to a(105) by _Antti Karttunen_, Jan 18 2025