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

Author

Michelle Huff, Oct 28 2016

Keywords

• nonn
• cons

Comments

The sum of four easily recognized geometric series that have common ratio 9/64.

An algebraic number with minimal polynomial 1369x^2 - 6216x + 6468. - Charles R Greathouse IV, Oct 29 2016

Examples

			2.92564084610714275971308780...
		

Links

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

Crossrefs

Cf. A010527, A277755.

Programs

Mathematica

r = Sqrt[3]/2; u = Simplify[r (1 + r + r^3 - r^4)/(1 - r^6)]
RealDigits[N[u, 120], 10][[1]]

PARI

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

PARI

(sqrt(3)+6)*14/37 \\ Charles R Greathouse IV, Oct 29 2016

Formula

Equals (14/37)*(6 + sqrt(3)).