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A246104 Least m > 0 for which (s(m), ..., s(n+m-1)) = (s(0), ..., s(n)), the first n+1 terms of the infinite Fibonacci word A003849.

%I A246104 #18 Jan 10 2024 16:02:06
%S A246104 2,3,5,5,8,8,8,13,13,13,13,13,21,21,21,21,21,21,21,21,34,34,34,34,34,
%T A246104 34,34,34,34,34,34,34,34,55,55,55,55,55,55,55,55,55,55,55,55,55,55,55,
%U A246104 55,55,55,55,55,55,89,89,89,89,89,89,89,89,89,89,89,89
%N A246104 Least m > 0 for which (s(m), ..., s(n+m-1)) = (s(0), ..., s(n)), the first n+1 terms of the infinite Fibonacci word A003849.
%C A246104 If n is a term of A001911, then a(n) = n+2, otherwise a(n) > n+2. - _Ivan Neretin_, Sep 30 2017
%H A246104 Ivan Neretin, <a href="/A246104/b246104.txt">Table of n, a(n) for n = 0..10944</a>
%F A246104 Concatenation of F(n - 2) copies of F(n), for n >= 1, where F = A000045 (Fibonacci numbers).
%e A246104 In A003849, the initial segment (s(0), ..., s(6)) = (0,1,0,0,1,0,1) first repeats at (s(8), ..., s(14)), so that a(6) = 8.
%p A246104 seq(combinat:-fibonacci(n)$combinat:-fibonacci(n-2),n=2..12); # _Robert Israel_, Oct 01 2017
%t A246104 s = Flatten[Nest[{#, #[[1]]} &, {0, 1}, 12]]; b[m_, n_] := b[m, n] = Take[s, {m, n}]; q = -1 + Flatten[Table[Select[n + Range[2, 1600], b[#, n + # - 1] == b[1, n] &, 1], {n, 1, 120}]]
%t A246104 Flatten@Table[ConstantArray[Fibonacci[n + 1], Fibonacci[n - 1]], {n, 10}] (* _Ivan Neretin_, Sep 30 2017 *)
%Y A246104 Cf. A000045, A003849, A241422, A246105.
%K A246104 nonn,easy
%O A246104 0,1
%A A246104 _Clark Kimberling_, Aug 14 2014