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A073012
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Decimal expansion of Robbins constant.
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8
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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, 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, 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
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OFFSET
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0,1
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COMMENTS
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The average distance between two points chosen at random inside a unit cube.
This constant was named after the American mathematician David Peter Robbins (1942 - 2003). - Amiram Eldar, Aug 25 2020
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 479.
Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 693.
Francois Le Lionnais, Les nombres remarquables, Paris: Hermann, 1983. See p. 30.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..5000
Simon Plouffe, The Robbins constant, in Miscellaneous Mathematical Constants, p. 173.
David P. Robbins, Problem E2629, The American Mathematical Monthly, Vol. 84, No. 1 (1977), p. 57, Theodore S. Bolis, Solution to problem E2629: Average distance between two points in a box, also solved by the proposer and by Günter Bach and Frank Piefke, ibid., Vol. 85, No. 4 (1978), pp. 277-278.
Eric Weisstein's World of Mathematics, Cube Line Picking.
Eric Weisstein's World of Mathematics, Hypercube Line Picking.
Eric Weisstein's World of Mathematics, Robbins Constant.
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FORMULA
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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
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EXAMPLE
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0.66170718226717623515583113324841358174640013579095...
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MATHEMATICA
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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]]
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PROG
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(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
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CROSSREFS
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Cf. A091505.
Sequence in context: A153605 A247447 A112302 * A102522 A201672 A200299
Adjacent sequences: A073009 A073010 A073011 * A073013 A073014 A073015
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KEYWORD
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cons,nonn
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AUTHOR
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Robert G. Wilson v, Aug 03 2002
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STATUS
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approved
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