A051017 Numbers n for which r^n-floor(r^n) > 1/2, where r is the real root of x^3-x-1.

2, 9, 10, 13, 15, 16, 18, 20, 21, 23, 26, 28, 31, 33, 34, 36, 39, 41, 44, 46, 47, 49, 51, 52, 54, 57, 59, 62, 64, 65, 67, 69, 70, 72, 75, 77, 80, 82, 83, 85, 87, 88, 90, 93, 95, 96, 98, 100, 101, 103, 106, 108, 111, 113, 114, 116, 118, 119, 121, 124, 126, 129, 131

Offset

1,1

Comments

For large powers, r^n is very close to an integer.

Links

Table of n, a(n) for n=1..63.

Eric Weisstein's World of Mathematics, Pisot Number

Mathematica

Flatten[ With[ {r = Root[ -1 - #1 + #1^3 &, 1 ]}, Position[ Table[ r^n - Floor[ r^n ], {n, 1, 200} ], _?(#1 > 1/2 & ), 1 ] ] ]

Crossrefs

Cf. A051016, A060006.

Sequence in context: A373261 A031443 A344145 * A078180 A058890 A369205

Adjacent sequences: A051014 A051015 A051016 * A051018 A051019 A051020

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Corrected by Don Reble, May 04 2006

Status

approved