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A086089 Decimal expansion of 3*sqrt(3)/(2*Pi). 5
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Limiting ratio of areas in the disk-covering problem.

From Daniel Forgues, May 26 2010: (Start)

Consider: A060544 (Centered 9-gonal numbers), starting with 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:

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)

The area of a regular hexagon circumscribed in a unit-area circle. - Amiram Eldar, Nov 05 2020

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, Sections 5.9 p. 325 and 8.2 p. 486.

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 196.

LINKS

Table of n, a(n) for n=0..101.

Veikko Nevanlinna, On constants connected with the prime number theorem for arithmetic progressions, Annales Academiae Scientiarum Fennicae Ser. A. I., No. 539 (1973).

FORMULA

Equals Product_{n>=1} (1 - 1/(3n)^2). - Bruno Berselli, Apr 02 2013

Equals sinc(Pi/3). - Peter Luschny, Oct 04 2019

Equals Product{k>=1} cos(Pi/(3*2^k)). - Amiram Eldar, Aug 20 2020

Equals Sum_{k>=0} mu(3*k+1)/(3*k+1) (Nevanlinna, 1973). - Amiram Eldar, Dec 21 2020

EXAMPLE

0.8269933431326880742669897474694541620960797205499609791990...

MATHEMATICA

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 *)

PROG

(PARI) 3*sqrt(3)/(2*Pi) \\ Michel Marcus, Nov 05 2020

CROSSREFS

Cf. A008683, A060544.

Sequence in context: A120219 A240976 A199158 * A091350 A099876 A153203

Adjacent sequences:  A086086 A086087 A086088 * A086090 A086091 A086092

KEYWORD

nonn,cons,easy

AUTHOR

Eric W. Weisstein, Jul 08 2003

STATUS

approved

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Last modified November 28 03:12 EST 2021. Contains 349400 sequences. (Running on oeis4.)