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n-th digit after decimal point of the successive approximations to phi = .618...; equally, n-th digit after decimal point of F(n)/F(n+1).
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%I #5 Dec 05 2013 19:57:14

%S 0,0,6,0,0,4,6,5,8,0,5,2,5,4,1,2,7,9,8,7,6,8,6,8,3,3,5,0,1,2,7,1,0,2,

%T 4,6,1,5,8,0,2,4,6,9,3,3,7,1,7,2,0,7,2,8,8,0,1,0,4,3,7,1,6,4,1,2,7,9,

%U 5,6,5,4,2,2,3,1,3,8,5,8,9,7,2,4,9,9,5,5,7,4,2,3,1,6,6,0,6,9,4,8,0,7,5,8,5

%N n-th digit after decimal point of the successive approximations to phi = .618...; equally, n-th digit after decimal point of F(n)/F(n+1).

%e 1/1 = 1.0

%e 1/2 = 0.50

%e 2/3 = 0.666...

%e 3/5 = 0.6000...

%e 5/8 = 0.62500

%e 8/13 = 0.615384...

%e 13/21 = 0.6190476...

%t f[n_] := RealDigits[ Fibonacci[n]/Fibonacci[n + 1], 10, 111][[1, n]]; Array[f, 105] (* _Robert G. Wilson v_ *)

%K base,nonn

%O 1,3

%A _Amarnath Murthy_, Nov 17 2005

%E More terms from _Robert G. Wilson v_, Jan 03 2006