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A130312
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Each Fibonacci number F(n) appears F(n) times.
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8
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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, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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Flatten[Table[#, {#}]&/@Fibonacci[Range[10]]] (* Harvey P. Dale, Apr 18 2012 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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