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A093577
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Decimal expansion of (3/4)*sqrt(2).
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3
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1, 0, 6, 0, 6, 6, 0, 1, 7, 1, 7, 7, 9, 8, 2, 1, 2, 8, 6, 6, 0, 1, 2, 6, 6, 5, 4, 3, 1, 5, 7, 2, 7, 3, 5, 5, 8, 9, 2, 7, 2, 5, 3, 9, 0, 6, 5, 3, 2, 7, 1, 1, 0, 5, 4, 8, 8, 2, 5, 0, 9, 8, 0, 3, 4, 9, 3, 0, 4, 9, 3, 5, 8, 8, 4, 6, 5, 8, 0, 2, 7, 9, 1, 3, 7, 7, 9, 0, 6, 5, 0, 7, 4, 5, 7, 3, 1, 1, 7, 9, 5, 5
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OFFSET
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1,3
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COMMENTS
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Side length of Prince Rupert's cube: the largest cube that can be passed through a given unit cube (slightly larger than the given cube!).
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REFERENCES
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Clifford A. Pickover, The Math Book, Sterling Publishing Co. (New York), 2009, p. 214.
D. J. E. Schrek, Prince Rupert's problem and its extension by Pieter Nieuwland, Scripta Math. 16 (1950), pp. 73-80 and 261-267.
David Wells, Penguin Dictionary of Curious and Interesting Geometry, 1991, p. 195.
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LINKS
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FORMULA
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Equals Sum_{k>=0} binomial(2*k,k)/36^k. - Amiram Eldar, Aug 04 2022
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EXAMPLE
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1.060660171779821286601266543157273558927253906532711...
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MATHEMATICA
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RealDigits[3 Sqrt[2]/4, 10, 110][[1]] (* Bruno Berselli, Sep 20 2012 *)
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PROG
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(Magma) SetDefaultRealField(RealField(100)); Sqrt(9/8); // G. C. Greubel, Aug 17 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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