A051016 Numbers n for which r^n-floor(r^n) < 1/2, where r is the real root of x^3-x-1.

1, 3, 4, 5, 6, 7, 8, 11, 12, 14, 17, 19, 22, 24, 25, 27, 29, 30, 32, 35, 37, 38, 40, 42, 43, 45, 48, 50, 53, 55, 56, 58, 60, 61, 63, 66, 68, 71, 73, 74, 76, 78, 79, 81, 84, 86, 89, 91, 92, 94, 97, 99, 102, 104, 105, 107, 109, 110, 112, 115, 117, 120, 122, 123, 125, 127

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

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

Links

• Eric Weisstein's World of Mathematics, Pisot Number

Crossrefs

Cf. A051017, A060006 (r = 1.32471...).

Programs

Mathematica

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

Extensions

Corrected by Don Reble, May 04 2006