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A010467 Decimal expansion of square root of 10. 32

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of square root of 10.

%C Continued fraction expansion is 3 followed by {6} repeated. - _Harry J. Smith_, Jun 02 2009

%C In 1594, Joseph Scaliger claimed Pi = sqrt(10), but Ludolph van Ceulen immediately knew this to be wrong. - _Alonso del Arte_, Jan 17 2013

%H Harry J. Smith, <a href="/A010467/b010467.txt">Table of n, a(n) for n = 1..20000</a>

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/sqrt_base">Index of expansions of sqrt(d) in base b</a>

%H R. J. Nemiroff & J. Bonnell, <a href="http://antwrp.gsfc.nasa.gov/htmltest/gifcity/sqrt10.1mil">The first 1 million digits of square root of 10</a>

%H R. J. Nemiroff & J. Bonnell, Plouffe's Inverter, <a href="http://www.plouffe.fr/simon/constants/sqrt10.txt">The first 1 million digits of square root of 10</a>

%H J. J. O'Connor and E. F. Robertson, <a href="http://www-history.mcs.st-and.ac.uk/Biographies/Van_Ceulen.html">Ludolph Van Ceulen</a>

%F Sqrt(10).

%F a(n) = -10*floor(10^(-(3/2) + n)) + floor(10^(-(1/2) + n)) for n > 0. - _Mariusz Iwaniuk_, Apr 26 2017

%e 3.162277660168379331998893544432718533719555139325216826857504852792594...

%e 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

%t RealDigits[N[Sqrt[10],200]] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2010 *)

%o (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

%Y Cf. A040006 (continued fraction).

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)