A277754 Decimal expansion of Sum_{n>=1} sin((n*Pi)/3)^n.
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, 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, 8, 2, 7, 6, 3, 1, 5, 4, 6, 8, 1, 0, 9, 5, 1, 1, 1, 7
Offset: 1
Examples
2.92564084610714275971308780...
Links
- Michelle Huff, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
r = Sqrt[3]/2; u = Simplify[r (1 + r + r^3 - r^4)/(1 - r^6)] RealDigits[N[u, 120], 10][[1]]
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PARI
suminf(n=1, sin((n*Pi)/3)^n) \\ Michel Marcus, Oct 29 2016
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PARI
(sqrt(3)+6)*14/37 \\ Charles R Greathouse IV, Oct 29 2016
Formula
Equals (14/37)*(6 + sqrt(3)).
Comments