A277755 Decimal expansion of Sum_{n>=1} |sin((n*Pi)/3)|^n.

4, 6, 1, 0, 8, 7, 9, 4, 6, 9, 6, 8, 7, 6, 7, 2, 0, 1, 8, 2, 8, 0, 3, 3, 2, 8, 9, 3, 9, 2, 6, 8, 5, 4, 5, 4, 9, 9, 2, 2, 7, 0, 9, 8, 0, 2, 4, 4, 6, 4, 6, 0, 3, 0, 8, 1, 8, 3, 5, 2, 2, 9, 4, 5, 2, 0, 5, 3, 1, 4, 8, 8, 7, 7, 1, 4, 5, 9, 4, 6, 4, 4, 7, 0, 4, 2

Offset: 1

Author

Michelle Huff, Oct 28 2016

Keywords

• nonn
• cons

Examples

			(2/37)*(42 + 25 Sqrt[3]) = 4.61087946968767201828033289392685454992..., the sum of two easily recognized geometric series that have common ratio (3/4)^(3/2).
		

Links

• Michelle Huff, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010527, A277754.

Programs

Mathematica

r = Sqrt[3]/2; u = Simplify[r (1 + r)/(1 - r^3)]
RealDigits[N[u, 1200], 10][[1]]

PARI

suminf(n=1, abs(sin((n*Pi)/3))^n) \\ Michel Marcus, Oct 29 2016