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A086089 Decimal expansion of 3*sqrt(3)/(2*Pi). 3

%I

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

%T 6,2,0,9,6,0,7,9,7,2,0,5,4,9,9,6,0,9,7,9,1,9,9,0,4,9,0,3,0,4,3,6,5,4,

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

%N Decimal expansion of 3*sqrt(3)/(2*Pi).

%C Limiting ratio of areas in the disk-covering problem.

%C From _Daniel Forgues_, May 26 2010: (Start)

%C Consider: A060544, Centered 9-gonal (or nonagonal) numbers, starting with

%C a(1)=1, P_c(9, n), n >= 1. Every third triangular number, starting with a(1)=1, P(3, 3n-2), n >= 1. Then:

%C 1/(sum_{n=0..infinity} 1/binomial(3n+2,2)) = 1/(sum_{n=1..infinity} 1/binomial(3n-1,2)) = 1/(sum_{n=1..infinity} 1/P_c(9,n)) = 1/(sum_{n=1..infinity} 1/P(3,3n-2)) = 1/(sum_{n=1..infinity} 1/A060544(n)) = this constant. (End)

%C Also, decimal expansion of product_{n>=1} (1 - 1/(3n)^2). [_Bruno Berselli_, Apr 02 2013]

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, Sections 5.9 p. 325 and 8.2 p. 486.

%F Equals sinc(Pi/3). - _Peter Luschny_, Oct 04 2019

%e 0.8269933431326880742669897474694541620960797205499609791990...

%t RealDigits[3 Sqrt[3]/(2 Pi), 10, 110][[1]] (* or, from the third comment: *) RealDigits[N[Product[1 - 1/(3 n)^2, {n, 1, Infinity}], 110]][[1]] (* _Bruno Berselli_, Apr 02 2013 *)

%Y Cf. A060544.

%K nonn,cons,easy

%O 0,1

%A _Eric W. Weisstein_, Jul 08 2003

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Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)