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%I #15 Aug 23 2021 00:36:13
%S 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,
%T 45,48,50,53,55,56,58,60,61,63,66,68,71,73,74,76,78,79,81,84,86,89,91,
%U 92,94,97,99,102,104,105,107,109,110,112,115,117,120,122,123,125,127
%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. A051017, A060006 (r = 1.32471...).
%K nonn
%O 1,2
%A _Eric W. Weisstein_
%E Corrected by _Don Reble_, May 04 2006