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%I #11 Apr 13 2018 07:32:50
%S 2,9,10,13,15,16,18,20,21,23,26,28,31,33,34,36,39,41,44,46,47,49,51,
%T 52,54,57,59,62,64,65,67,69,70,72,75,77,80,82,83,85,87,88,90,93,95,96,
%U 98,100,101,103,106,108,111,113,114,116,118,119,121,124,126,129,131
%N Numbers n for which r^n-floor(r^n) > 1/2, where r is the real root of x^3-x-1.
%C For large powers, r^n is very close to an integer.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>
%t Flatten[ With[ {r = Root[ -1 - #1 + #1^3 &, 1 ]}, Position[ Table[ r^n - Floor[ r^n ], {n, 1, 200} ], _?(#1 > 1/2 & ), 1 ] ] ]
%Y Cf. A051016, A060006.
%K nonn
%O 1,1
%A _Eric W. Weisstein_
%E Corrected by _Don Reble_, May 04 2006
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