A072648 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.

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, 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, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..88.

Maple

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

Prog

(Scheme function:) (define (A072648 n) (cond ((zero? n) n) (else (floor->exact (/ (log (* n *Sqrt5*)) *LogPhi*)))))
(define *Sqrt5* (sqrt 5))
(define *Phi* (/ (1+ *Sqrt5*) 2))
(define *LogPhi* (log *Phi*))

Crossrefs

Used to construct A072649.

Sequence in context: A196337 A349784 A298200 * A185585 A072945 A307912

Adjacent sequences: A072645 A072646 A072647 * A072649 A072650 A072651

Keyword

nonn

Author

Antti Karttunen, Jun 02 2002

Status

approved