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A010467 Decimal expansion of square root of 10. 43
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
REFERENCES
Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 27.
LINKS
Josep M. Brunat and Joan-Carles Lario, A problem on concatenated integers, arXiv:2103.05306 [math.NT], 2021. For 1/sqrt(10).
Robert Nemiroff and Jerry Bonnell, The first 1 million digits of square root of 10.
Robert Nemiroff and Jerry Bonnell, Plouffe's Inverter, The first 1 million digits of square root of 10.
J. J. O'Connor and E. F. Robertson, Ludolph Van Ceulen.
FORMULA
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 1/sqrt(10), with offset 0. - Michel Marcus, Mar 10 2021
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
EXAMPLE
3.162277660168379331998893544432718533719555139325216826857504852792594...
MATHEMATICA
RealDigits[N[Sqrt[10], 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)
PROG
(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
CROSSREFS
Cf. A000032, A040006 (continued fraction).
Sequence in context: A181187 A104573 A327438 * A335320 A182182 A158823
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 19 03:21 EDT 2024. Contains 370952 sequences. (Running on oeis4.)