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 A010466 Decimal expansion of square root of 8. 37

%I

%S 2,8,2,8,4,2,7,1,2,4,7,4,6,1,9,0,0,9,7,6,0,3,3,7,7,4,4,8,4,1,9,3,9,6,

%T 1,5,7,1,3,9,3,4,3,7,5,0,7,5,3,8,9,6,1,4,6,3,5,3,3,5,9,4,7,5,9,8,1,4,

%U 6,4,9,5,6,9,2,4,2,1,4,0,7,7,7,0,0,7,7,5,0,6,8,6,5,5,2,8,3,1,4,5,4,7

%N Decimal expansion of square root of 8.

%C Sqrt(8)=2*sqrt(2) is the length of the longest (rigid) ladder that can be carried horizontally around a right angled corner in a hallway of unit width. - _Lekraj Beedassy_, Apr 19 2006

%C Continued fraction expansion is 2 followed by {1, 4} repeated. - _Harry J. Smith_, Jun 05 2009

%C This is the second Lagrange number. - _Alonso del Arte_, Dec 06 2011

%C Also 2*sqrt(2) is the ratio of the perimeter of a square to its diameter (diagonal length). - _Rick L. Shepherd_, Dec 29 2016

%C Uchiyama shows that every interval (n, n + c*n^(1/4)) contains an integer that is the sum of two squares, where c = 2^(3/2). - _Michel Marcus_, Jan 03 2018

%D S. R. Finch, Moving Sofa Constant, Sect. 8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.

%H Harry J. Smith, <a href="/A010466/b010466.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/sqrt8.1mil">The first 1 million digits of the square root of 8</a>

%H R. J. Nemiroff & J. Bonnell, Plouffe's Inverter, <a href="http://www.cecm.sfu.ca/projects/ISC/dataB/isc/C/sqrt8.txt">The first 1 million digits of the square root of 8</a>

%H S. Uchiyama, <a href="http://hdl.handle.net/2115/56058">On the distribution of integers representable as a sum of two h-th powers</a>, J. Fac. Sci. Hokkaido Univ. Ser. I, 18, 124-127, 1964/1965.

%F Equals 1 + Sum_{n>=1} ( Product_{k=1..n} (2k+1)/(4k) ). [_Bruno Berselli_, Mar 16 2014]

%e 2.828427124746190097603377448419396157139343750753896146353359475981464...

%e Sqrt(8) = sqrt(1+2*i*sqrt(2)) + sqrt(1-2*i*sqrt(2)) = sqrt(1/2+2*i*sqrt(3)) + sqrt(1/2-2*i*sqrt(3)), where i=sqrt(-1). [_Bruno Berselli_, Nov 20 2012]

%e 1 + 3/4 + 3*5/(4*8) + 3*5*7/(4*8*12) + 3*5*7*9/(4*8*12*16) + ... [_Bruno Berselli_, Mar 16 2014]

%p evalf(2^(3/2)) ; # _R. J. Mathar_, Jul 15 2013

%t RealDigits[N[Sqrt,200]][] (* _Vladimir Joseph Stephan Orlovsky_, Mar 04 2011 *)

%o (PARI) { default(realprecision, 20080); x=sqrt(8); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010466.txt", n, " ", d)); } \\ _Harry J. Smith_, Jun 02 2009

%Y Cf. A040005 (continued fraction).

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_

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Last modified November 16 20:13 EST 2019. Contains 329206 sequences. (Running on oeis4.)