A109918 - OEIS

%I #12 Jan 11 2020 00:35:15

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

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

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

%N n-th digit after decimal point in phi^n, where phi = (1 + sqrt(5))/2.

%C phi^2-phi=1, so phi^2 and phi have the same digits after the decimal point. Can someone find a number k in which the n-th digit after the decimal point in k^n is constant or follows a pattern?

%t a[n_] := Block[{rd = RealDigits[ GoldenRatio^n, 10, 200]}, rd[[1, rd[[2]] + n]]]; Table[ a[n], {n, 105}] (* _Robert G. Wilson v_, Jul 19 2005 *)

%Y Cf. A001622 (golden ratio).

%K base,easy,nonn

%O 1,1

%A _Amarnath Murthy_, Jul 16 2005

%E More terms from _Robert G. Wilson v_, Jul 19 2005