A109918 n-th digit after decimal point in phi^n, where phi = (1 + sqrt(5))/2.

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, 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, 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

Offset

1,1

Comments

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?

Links

Table of n, a(n) for n=1..105.

Mathematica

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 *)

Crossrefs

Cf. A001622 (golden ratio).

Sequence in context: A344699 A010687 A176355 * A339433 A263494 A096956

Adjacent sequences: A109915 A109916 A109917 * A109919 A109920 A109921

Keyword

base,easy,nonn

Author

Amarnath Murthy, Jul 16 2005

Extensions

More terms from Robert G. Wilson v, Jul 19 2005

Status

approved