A113555 - OEIS

%I #8 Mar 02 2023 13:21:50

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

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

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

%N n-th digit after decimal of the successive approximation of the golden ratio. n-th digit after decimal of F(n+1)/F(n).

%H G. C. Greubel, <a href="/A113555/b113555.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7) = 6, F(8)/F(7) =21/13 = 1.615384 6 153846153846153846153846...

%t i = 1; While[i < 100, Print[N[Fibonacci[i + 1]/Fibonacci[i], i + 4]] i++ ] (McVey)

%t Array[Function[n, RealDigits[N[Fibonacci[n + 1]/Fibonacci[n], n+3]] // (#[[1, #[[2]] + n]]) &], 100] (* _G. C. Greubel_, Aug 31 2018 *)

%t Join[{0},Table[RealDigits[Fibonacci[n+1]/Fibonacci[n],10,200][[1]][[n+1]],{n,2,100}]] (* _Harvey P. Dale_, Mar 02 2023 *)

%K base,easy,nonn

%O 1,4

%A _Amarnath Murthy_, Nov 06 2005

%E More terms from Ryan McVey (rwm185(AT)psu.edu), Jan 24 2006