A072648 - OEIS

%I #3 May 01 2014 02:43:29

%S 1,3,3,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,

%T 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,

%U 10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10

%N a(n) = [log_{Phi}(n*sqrt(5))], where log_{Phi} is logarithm in the base Phi ( = (sqrt(5)+1)/2) and [] stands for the floor function.

%C An approximate "inverse" of A000045 (of the Fibonacci numbers).

%p [seq(floor(log[(sqrt(5)+1)/2](n*sqrt(5))),n=1..120)];

%o (Scheme function:) (define (A072648 n) (cond ((zero? n) n) (else (floor->exact (/ (log (* n *Sqrt5*)) *LogPhi*)))))

%o (define *Sqrt5* (sqrt 5))

%o (define *Phi* (/ (1+ *Sqrt5*) 2))

%o (define *LogPhi* (log *Phi*))

%Y Used to construct A072649.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 02 2002