

A051016


Numbers n for which r^nfloor(r^n) < 1/2, where r is the real root of x^3x1.


6



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..66.
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. A051017.
Sequence in context: A047563 A261604 A120561 * A044951 A138308 A039084
Adjacent sequences: A051013 A051014 A051015 * A051017 A051018 A051019


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


EXTENSIONS

Corrected by Don Reble, May 04 2006


STATUS

approved



