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%I #20 Nov 08 2016 07:44:15
%S 2,9,2,5,6,4,0,8,4,6,1,0,7,1,4,2,7,5,9,7,1,3,0,8,7,8,0,4,8,9,4,1,1,3,
%T 8,6,8,5,7,2,9,5,3,3,3,9,2,7,9,6,0,3,4,8,0,8,8,5,9,8,1,0,1,9,2,5,2,0,
%U 8,2,7,6,3,1,5,4,6,8,1,0,9,5,1,1,1,7
%N Decimal expansion of Sum_{n>=1} sin((n*Pi)/3)^n.
%C The sum of four easily recognized geometric series that have common ratio 9/64.
%C An algebraic number with minimal polynomial 1369x^2 - 6216x + 6468. - _Charles R Greathouse IV_, Oct 29 2016
%H Michelle Huff, <a href="/A277754/b277754.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals (14/37)*(6 + sqrt(3)).
%e 2.92564084610714275971308780...
%t r = Sqrt[3]/2; u = Simplify[r (1 + r + r^3 - r^4)/(1 - r^6)]
%t RealDigits[N[u, 120], 10][[1]]
%o (PARI) suminf(n=1, sin((n*Pi)/3)^n) \\ _Michel Marcus_, Oct 29 2016
%o (PARI) (sqrt(3)+6)*14/37 \\ _Charles R Greathouse IV_, Oct 29 2016
%Y Cf. A010527, A277755.
%K nonn,cons
%O 1,1
%A _Michelle Huff_, Oct 28 2016
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