A093577 Decimal expansion of (3/4)*sqrt(2).

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

Offset

1,3

Comments

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!).

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.14, p. 524.

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.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prince Rupert's Cube.

Index entries for algebraic numbers, degree 2.

Formula

Equals Sum_{k>=0} binomial(2*k,k)/36^k. - Amiram Eldar, Aug 04 2022

Example

1.060660171779821286601266543157273558927253906532711...

Mathematica

RealDigits[3 Sqrt[2]/4, 10, 110][[1]] (* Bruno Berselli, Sep 20 2012 *)

Prog

(PARI) sqrt(9/8) \\ Charles R Greathouse IV, Nov 26 2014
(Magma) SetDefaultRealField(RealField(100)); Sqrt(9/8); // G. C. Greubel, Aug 17 2018

Crossrefs

Sequence in context: A092605 A180318 A004016 * A065442 A368501 A198752

Adjacent sequences: A093574 A093575 A093576 * A093578 A093579 A093580

Keyword

nonn,cons

Author

Eric W. Weisstein, Apr 01 2004

Status

approved