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%I #28 Aug 25 2020 04:25:06
%S 6,6,1,7,0,7,1,8,2,2,6,7,1,7,6,2,3,5,1,5,5,8,3,1,1,3,3,2,4,8,4,1,3,5,
%T 8,1,7,4,6,4,0,0,1,3,5,7,9,0,9,5,3,6,0,4,8,0,8,9,4,4,2,2,9,4,7,9,5,8,
%U 4,6,4,6,1,3,8,5,9,7,6,3,1,3,0,6,6,5,2,4,8,0,7,6,8,1,0,7,1,2,0,1,5,1,7,0,9
%N Decimal expansion of Robbins constant.
%C The average distance between two points chosen at random inside a unit cube.
%C This constant was named after the American mathematician David Peter Robbins (1942 - 2003). - _Amiram Eldar_, Aug 25 2020
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 479.
%D Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 693.
%D Francois Le Lionnais, Les nombres remarquables, Paris: Hermann, 1983. See p. 30.
%H G. C. Greubel, <a href="/A073012/b073012.txt">Table of n, a(n) for n = 0..5000</a>
%H Simon Plouffe, <a href="https://www.sapili.org/livros/en/gu000634.pdf">The Robbins constant</a>, in Miscellaneous Mathematical Constants, p. 173.
%H David P. Robbins, <a href="http://www.jstor.org/stable/2318315">Problem E2629</a>, The American Mathematical Monthly, Vol. 84, No. 1 (1977), p. 57, Theodore S. Bolis, <a href="http://www.jstor.org/stable/2321177">Solution to problem E2629: Average distance between two points in a box</a>, also solved by the proposer and by Günter Bach and Frank Piefke, ibid., Vol. 85, No. 4 (1978), pp. 277-278.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubeLinePicking.html">Cube Line Picking</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HypercubeLinePicking.html">Hypercube Line Picking</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RobbinsConstant.html">Robbins Constant</a>.
%F 4/105 + (17/105) * sqrt(2) - (2/35) * sqrt(3) + (1/5) * log(1+sqrt(2)) + (2/5) * log(2+sqrt(3)) - (1/15) * Pi. - _Eric W. Weisstein_, Mar 02 2005
%e 0.66170718226717623515583113324841358174640013579095...
%t RealDigits[ N[4/105 + 17/105*Sqrt[2] - 2/35*Sqrt[3] + 1/5*Log[1 + Sqrt[2]] + 2/5*Log[2 + Sqrt[3]] - 1/15*Pi, 110]] [[1]]
%o (PARI) (4 + 17*sqrt(2) - 6*sqrt(3) + 21*log(1 + sqrt(2)) + 42*log(2 + sqrt(3)) - 7*Pi)/105 \\ _G. C. Greubel_, Jan 11 2017
%Y Cf. A091505.
%K cons,nonn
%O 0,1
%A _Robert G. Wilson v_, Aug 03 2002
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