A089961 - OEIS

%I #8 May 12 2013 03:08:08

%S 3,4,7,3,11,3,3,18,3,5,5,3,29,3,4,9,3,8,4,3,47,3,4,6,3,14,3,3,13,3,6,

%T 4,3,76,3,4,7,3,9,3,3,23,3,5,5,3,21,3,3,10,3,7,4,3,123,3,4,6,3,12,3,3,

%U 15,3,6,5,3,38,3

%N a(n) = floor( 1/( {n/phi}-{n/phi}^2 ) )-1, where {} is the fractional part and phi the golden ratio.

%C a(Fibonacci(n)) = Lucas(n), n>=2, where Fibonacci=A000045 and Lucas=A000032.

%C a(Lucas(n)) = Fibonacci(n), n>=4.

%C Examples: a(8) = 18, where 8 = Fibonacci(6) and 18 = Lucas(6). a(29) = 13, where 29 = Lucas(7) and 13 = Fibonacci(7).

%F a(n) = A089959(n) - 1.

%p fpart := proc(x)

%p         x-floor(x) ;

%p end proc:

%p A089961 := proc(n)

%p     invphi := 2/(1+sqrt(5)) ;

%p     fn := fpart(n*invphi) ;

%p     1/fn/(1-fn);

%p     floor(%)-1 ;

%p end proc: # _R. J. Mathar_, May 11 2013

%Y Cf. A001622, A089959.

%K nonn

%O 1,1

%A _Gary W. Adamson_, Nov 20 2003