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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). Index entries for transcendental numbers 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: A367899 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 February 29 02:52 EST 2024. Contains 370401 sequences. (Running on oeis4.)