Search: id:A072649
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%I A072649
%S A072649 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,
%T A072649 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,
%U A072649 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
%N A072649 n occurs A000045(n) times.
%C A072649 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
%C A072649 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.
%C A072649 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
%C A072649 The smallest non-decreasing sequence a(n) such that a(Fibonacci(n-1)) 
               = n. - Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 20 2007
%F A072649 G.f.: (Sum_{n>1} x^fibonacci(n))/(1-x). - Michael Somos, Apr 25, 2003
%F A072649 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
%F A072649 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
%e A072649 1, 1, then F(2) 2's, then F(3) 3's, then F(4) 4's, ..., then F(k) k's, 
               ...
%t A072649 Table[Table[n, {Fibonacci[n]}], {n, 10}] // Flatten (* Robert G. Wilson 
               v (rgwv(AT)rgwv.com), Jan 14 2007 *)
%o A072649 (PARI) a(n) = -1+floor(log(((n+0.2)*sqrt(5)))/log((1+sqrt(5))/2))
%o A072649 (PARI) a(n)=local(m); if(n<1,0,m=0; until(fibonacci(m)>n,m++); m-2)
%o A072649 (MIT Scheme) (define (A072649 n) (let ((b (A072648 n))) (+ -1 b (floor->
               exact (/ n (A000045 (1+ b)))))))
%Y A072649 Cf. A000045, A095791, A095792.
%Y A072649 Used to construct A003714. Cf. also A002024, A072643, A072648, A072650.
%Y A072649 Cf. A131234.
%Y A072649 Sequence in context: A029118 A129382 A163515 this_sequence A105195 A039836 
               A083398
%Y A072649 Adjacent sequences: A072646 A072647 A072648 this_sequence A072650 A072651 
               A072652
%K A072649 nonn
%O A072649 1,2
%A A072649 Antti Karttunen Jun 02 2002
%E A072649 Typo fixed by Charles R Greathouse IV (charles.greathouse(AT)case.edu), 
               Oct 28 2009

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