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Search: id:A002194
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| A002194 |
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Decimal expansion of square root of 3.
(Formerly M4326 N1812)
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+0
22
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| 1, 7, 3, 2, 0, 5, 0, 8, 0, 7, 5, 6, 8, 8, 7, 7, 2, 9, 3, 5, 2, 7, 4, 4, 6, 3, 4, 1, 5, 0, 5, 8, 7, 2, 3, 6, 6, 9, 4, 2, 8, 0, 5, 2, 5, 3, 8, 1, 0, 3, 8, 0, 6, 2, 8, 0, 5, 5, 8, 0, 6, 9, 7, 9, 4, 5, 1, 9, 3, 3, 0, 1, 6, 9, 0, 8, 8, 0, 0, 0, 3, 7, 0, 8, 1, 1, 4, 6, 1, 8, 6, 7, 5, 7, 2, 4, 8, 5, 7, 5, 6, 7, 5, 6, 2, 6, 1, 4, 1, 4, 1, 5, 4
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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"The square root of 3, the 2nd number, after root 2, to be proved irrational, by Theodorus."
Length of a diagonal between any vertex of the unit cube and the one corresponding (opposite) vertex not part of the three faces meeting at the original vertex. (Diagonal is hypotenuse of a triangle with sides 1 and sqrt(2)). Hence the diameter of the sphere circumscribed around the unit cube; the ratio of the diameter of any sphere to the edge length of its inscribed cube. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 09 2005
The square root of 3 is the length of the minimal Y-shaped (symmetrical) network linking three points unit distance apart. - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 12 2006
Continued fraction expansion is 1 followed by {1, 2} repeated. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
M. F. Jones, 22900D approximations to the square roots of the primes less than 100, Math. Comp., 22 (1968), 234-235.
Uhler, Horace S.; Approximations exceeding $1300$ decimals for sqrt 3, 1/sqrt 3, sin(pi/3) and distribution of digits in them. Proc. Nat. Acad. Sci. U. S. A. 37, (1951). 443-447.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 23.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
R. J. Nemiroff and J. Bonnell, The first 1 million digits of the square root of 3
S. Plouffe, Plouffe's Inverter, The square root of 3 to 10 million digits
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Theodorus's Constant
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EXAMPLE
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1.73205080756887729352744634150587236694280525381038062805580697945193301690880\
0037081146186757248575675626141415406703029969945094998952478811655512094373648\
5280932319023055820679748201010846749232650153123432669033228866506722546689218\
3797122704713166036786158801904998653737985938946765034750657605...
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MATHEMATICA
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RealDigits[ N[ Sqrt[3], 100]] [[1]]
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PROGRAM
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(PARI) { default(realprecision, 20080); x=(sqrt(3)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002194.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
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CROSSREFS
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Cf. A040001 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
Sequence in context: A021899 A133722 A160390 this_sequence A033327 A024584 A132713
Adjacent sequences: A002191 A002192 A002193 this_sequence A002195 A002196 A002197
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KEYWORD
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cons,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 07 2000
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