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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
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
Sequence in context: A367899 A240976 A199158 * A091350 A099876 A153203
KEYWORD
nonn,cons,easy
AUTHOR
Eric W. Weisstein, Jul 08 2003
STATUS
approved

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Last modified February 29 02:52 EST 2024. Contains 370401 sequences. (Running on oeis4.)