cp's OEIS Frontend

A130312 Each Fibonacci number F(n) appears F(n) times.

%I A130312 #39 Nov 23 2024 16:46:35
%S A130312 1,1,2,2,3,3,3,5,5,5,5,5,8,8,8,8,8,8,8,8,13,13,13,13,13,13,13,13,13,
%T A130312 13,13,13,13,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,
%U A130312 21,21,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34,34
%N A130312 Each Fibonacci number F(n) appears F(n) times.
%C A130312 Also n-1-s(n-1), where s(n) is the length of the longest proper suffix of p, the length-n prefix of the infinite Fibonacci word (A003849), that appears twice in p. - _Jeffrey Shallit_, Mar 20 2017
%C A130312 a(n+1) = the least period of the length-n prefix of the infinite Fibonacci word (A003849).  A period of a length-n word x is an integer p, 1 <= p <= n such that x[i] = x[i+p] for 1 <= i <= n-p. - _Jeffrey Shallit_, May 23 2020
%C A130312 a(n) is the largest term in dual Zeckendorf representation of n-1 (A104326), for n >= 2. - _Amiram Eldar_, Aug 09 2024
%F A130312 a(n) = A000045(A072649(n)). - _Michel Marcus_, Aug 03 2022
%e A130312 As triangle:
%e A130312    1;
%e A130312    1;
%e A130312    2,  2;
%e A130312    3,  3,  3;
%e A130312    5,  5,  5,  5,  5;
%e A130312    8,  8,  8,  8,  8,  8,  8,  8;
%e A130312   13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13;
%e A130312   ...
%p A130312 T:= n-> (f-> f$f)((<<0|1>, <1|1>>^n)[1,2]):
%p A130312 seq(T(n), n=1..10);  # _Alois P. Heinz_, Nov 23 2024
%t A130312 Flatten[Table[#,{#}]&/@Fibonacci[Range[10]]] (* _Harvey P. Dale_, Apr 18 2012 *)
%o A130312 (Python)
%o A130312 from itertools import islice
%o A130312 def A130312_gen(): # generator of terms
%o A130312     a, b = 1, 1
%o A130312     while True:
%o A130312         yield from (a,)*a
%o A130312         a, b = b, a+b
%o A130312 A130312_list = list(islice(A130312_gen(),20)) # _Chai Wah Wu_, Oct 13 2022
%o A130312 (Python)
%o A130312 def A130312(n):
%o A130312     a, b = 0, 1
%o A130312     while (c:=a+b) <= n: a, b = b, c
%o A130312     return a # _Chai Wah Wu_, Nov 23 2024
%o A130312 (PARI) a(n) = my(m=0); until(fibonacci(m)>n, m++); fibonacci(m-2); \\ _Michel Marcus_, Nov 26 2022
%Y A130312 Cf. A000045, A003849, A072649, A104326.
%K A130312 nonn,easy,tabf
%O A130312 1,3
%A A130312 _Edwin F. Sampang_, May 21 2007
%E A130312 More terms from _Harvey P. Dale_, Apr 18 2012