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A010467
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Decimal expansion of square root of 10.
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43
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3, 1, 6, 2, 2, 7, 7, 6, 6, 0, 1, 6, 8, 3, 7, 9, 3, 3, 1, 9, 9, 8, 8, 9, 3, 5, 4, 4, 4, 3, 2, 7, 1, 8, 5, 3, 3, 7, 1, 9, 5, 5, 5, 1, 3, 9, 3, 2, 5, 2, 1, 6, 8, 2, 6, 8, 5, 7, 5, 0, 4, 8, 5, 2, 7, 9, 2, 5, 9, 4, 4, 3, 8, 6, 3, 9, 2, 3, 8, 2, 2, 1, 3, 4, 4, 2, 4, 8, 1, 0, 8, 3, 7, 9, 3, 0, 0, 2, 9
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OFFSET
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1,1
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COMMENTS
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Continued fraction expansion is 3 followed by {6} repeated. - Harry J. Smith, Jun 02 2009
In 1594, Joseph Scaliger claimed Pi = sqrt(10), but Ludolph van Ceulen immediately knew this to be wrong. - Alonso del Arte, Jan 17 2013
The 7th-century Hindu mathematician Brahmagupta used this constant as value of Pi. - Stefano Spezia, Jul 08 2022
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REFERENCES
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Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 27.
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LINKS
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FORMULA
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Sqrt(10) = sqrt(1 + i*sqrt(15)) + sqrt(1 - i*sqrt(15)) = sqrt(1/2 + 2*i*sqrt(5)) + sqrt(1/2 - 2*i*sqrt(5)), where i = sqrt(-1). - Bruno Berselli, Nov 20 2012
Equals 2 + Sum_{k>=1} Lucas(k)*binomial(2*k,k)/8^k. - Amiram Eldar, Jan 17 2022
a(k) = floor(Sum_{n>=1} A005875(n)/exp(Pi*n/(10^((2/3)*k+(1/3))))) mod 10. Will give the k-th decimal digit of sqrt(10). A005875 : number of ways to write n as sum of 3 squares. - Simon Plouffe, Dec 30 2023
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EXAMPLE
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3.162277660168379331998893544432718533719555139325216826857504852792594...
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 20080); x=sqrt(10); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010467.txt", n, " ", d)); \\ Harry J. Smith, Jun 02 2009
(Magma) SetDefaultRealField(RealField(100)); Sqrt(10); // Vincenzo Librandi, Feb 15 2020
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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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