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A072649
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n occurs A000045(n) times.
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23
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1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of digits in Zeckendorf-binary representation of n. E.g. the Zeckendorf representation of 12 is 8+3+1, which in binary notation is 10101, which consists of 5 digits. - Clark Kimberling (ck6(AT)evansville.edu), Jun 05 2004
First position where value n occurs is A000045(n+1), i.e. a(A000045(n)) = n-1, for n >= 2 and a(A000045(n)-1) = n-2, for n >= 3.
This is the number of distinct Fibonacci numbers greater than 0 which are less than or equal to n. - Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 10 2006
The smallest non-decreasing sequence a(n) such that a(Fibonacci(n-1)) = n. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 20 2007
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| G.f.: (Sum_{n>1} x^fibonacci(n))/(1-x). - Michael Somos, Apr 25, 2003
a(n)=floor(log_phi((sqr(5)*n+sqr(5*n^2+4))/2))-1, n>=1, where phi is the golden ratio. Alternatively, a(n)=floor(arsinh(sqr(5)*n/2)/ln(phi))-1. Also a(n)=A108852(n)-2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 02 2007
a(n) = -1 + floor[ log_phi( (n+0.2)*sqrt(5) ) ], where log_phi(x) is the logarithm to the base (1+sqrt(5))/2. - Ralf Stephan, May 14 2007
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EXAMPLE
| 1, 1, then F(2) 2's, then F(3) 3's, then F(4) 4's, ..., then F(k) k's, ...
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MATHEMATICA
| Table[Table[n, {Fibonacci[n]}], {n, 10}] // Flatten (* Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 14 2007 *)
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PROG
| (PARI) a(n) = -1+floor(log(((n+0.2)*sqrt(5)))/log((1+sqrt(5))/2))
(PARI) a(n)=local(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2)
(MIT Scheme) (define (A072649 n) (let ((b (A072648 n))) (+ -1 b (floor->exact (/ n (A000045 (1+ b)))))))
(Haskell)
a072649 n = a072649_list !! (n-1)
a072649_list = f 1 where
f n = (replicate (fromInteger $ a000045 n) n) ++ f (n+1)
-- Reinhard Zumkeller, Jul 04 2011
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CROSSREFS
| Cf. A000045, A095791, A095792.
Used to construct A003714. Cf. also A002024, A072643, A072648, A072650.
Cf. A131234.
Sequence in context: A029118 A129382 A163515 * A105195 A039836 A083398
Adjacent sequences: A072646 A072647 A072648 * A072650 A072651 A072652
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen Jun 02 2002
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EXTENSIONS
| Typo fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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