%I #11 Aug 03 2014 14:01:32
%S 0,3,5,6,8,10,11,13,16,18,21,23,24,26,28,29,31,34,36,39,41,42,44,46,
%T 47,49,52,54,55,57,59,60,62,65,67,70,72,73,75,77,78,80,83,85,88,90,91,
%U 93,95,96,98,101,103,106,108,109,111,114,116,119,121,122,124
%N Indices n such that Padovan(n) > R^n/(2*R+3) where R is the only real root of the polynomial x^3-x-1.
%C R is plastic number (A060006).
%e For n=24, Padovan(24) = 151 > 150.99309... = R^24/(2*R+3).
%t lim = 200; R = Solve[x^3 - x - 1 == 0, x][[1, 1, 2]]; powers = Table[Floor[R^n/(2*R + 3)], {n, 0, lim}]; p = CoefficientList[Series[(1 - x^2)/(1 - x^2 - x^3), {x, 0, lim}], x]; Select[Range[lim+1], p[[#]] > powers[[#]] &] - 1 (* _T. D. Noe_, Aug 01 2011 *)
%Y Cf. A000931, A060006.
%K nonn
%O 0,2
%A _Francesco Daddi_, Jul 31 2011