OFFSET
1,3
COMMENTS
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
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
a(n) is the largest term in dual Zeckendorf representation of n-1 (A104326), for n >= 2. - Amiram Eldar, Aug 09 2024
FORMULA
MATHEMATICA
Flatten[Table[#, {#}]&/@Fibonacci[Range[10]]] (* Harvey P. Dale, Apr 18 2012 *)
PROG
(Python)
from itertools import islice
def A130312_gen(): # generator of terms
a, b = 1, 1
while True:
yield from (a, )*a
a, b = b, a+b
(PARI) a(n) = my(m=0); until(fibonacci(m)>n, m++); fibonacci(m-2); \\ Michel Marcus, Nov 26 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Edwin F. Sampang, May 21 2007
EXTENSIONS
More terms from Harvey P. Dale, Apr 18 2012
STATUS
approved