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.

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, 34, 34, 34, 34, 34, 34, 34, 34, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89

Offset

0,1

Comments

If n is a term of A001911, then a(n) = n+2, otherwise a(n) > n+2. - Ivan Neretin, Sep 30 2017

Links

Ivan Neretin, Table of n, a(n) for n = 0..10944

Formula

Concatenation of F(n - 2) copies of F(n), for n >= 1, where F = A000045 (Fibonacci numbers).

Example

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.

Maple

seq(combinat:-fibonacci(n)$combinat:-fibonacci(n-2), n=2..12); # Robert Israel, Oct 01 2017

Mathematica

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}]]
Flatten@Table[ConstantArray[Fibonacci[n + 1], Fibonacci[n - 1]], {n, 10}] (* Ivan Neretin, Sep 30 2017 *)

Crossrefs

Cf. A000045, A003849, A241422, A246105.

Sequence in context: A067284 A353272 A123339 * A256654 A204926 A256663

Adjacent sequences: A246101 A246102 A246103 * A246105 A246106 A246107

Keyword

nonn,easy

Author

Clark Kimberling, Aug 14 2014

Status

approved