A073012 Decimal expansion of Robbins constant.
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
Offset: 0
Examples
0.66170718226717623515583113324841358174640013579095...
References
- 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.
Links
- 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.
- Wikipedia, Robbins constant.
Programs
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Mathematica
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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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
Formula
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
Comments