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 A010466 Decimal expansion of square root of 8. 37
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 Continued fraction expansion is 2 followed by {1, 4} repeated. - Harry J. Smith, Jun 05 2009 This is the second Lagrange number. - Alonso del Arte, Dec 06 2011 Also 2*sqrt(2) is the ratio of the perimeter of a square to its diameter (diagonal length). - Rick L. Shepherd, Dec 29 2016 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 This is the area of the eight-smallest triangle with integer side lengths (2, 3, 3), or the seventh-smallest triangle if two smaller triangles with the same area are counted only once (see A331251). - Hugo Pfoertner, Feb 12 2020 Diameter of a sphere whose surface area equals 8*Pi. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - Omar E. Pol, Feb 13 2020 Sqrt(8) = area between the curves y = sin x and y = cos x for Pi/4 < x < 5 Pi/4; this is one of infinitely many congruent convex regions bounded by the two curves. - Clark Kimberling, May 03 2020 REFERENCES S. R. Finch, Moving Sofa Constant, Sect. 8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003. LINKS Harry J. Smith, Table of n, a(n) for n = 1..20000 Jason Kimberley, Index of expansions of sqrt(d) in base b R. J. Nemiroff & J. Bonnell, The first 1 million digits of the square root of 8 R. J. Nemiroff & J. Bonnell, Plouffe's Inverter, The first 1 million digits of the square root of 8 [Broken link] S. Uchiyama, On the distribution of integers representable as a sum of two h-th powers, J. Fac. Sci. Hokkaido Univ. Ser. I, 18, 124-127, 1964/1965. Eric Weisstein's World of Mathematics, Moving Ladder Problem FORMULA Equals 1 + Sum_{n>=1} ( Product_{k=1..n} (2k+1)/(4k) ). - Bruno Berselli, Mar 16 2014 EXAMPLE 2.828427124746190097603377448419396157139343750753896146353359475981464... 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 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 MAPLE evalf(2^(3/2)) ; # R. J. Mathar, Jul 15 2013 MATHEMATICA RealDigits[N[Sqrt, 200]][] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *) PROG (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 (MAGMA) SetDefaultRealField(RealField(100)); Sqrt(8); // Vincenzo Librandi, Feb 13 2020 CROSSREFS Cf. A040005 (continued fraction). Cf. A331250, A331251. Sequence in context: A064912 A010698 A286309 * A086396 A195844 A222828 Adjacent sequences:  A010463 A010464 A010465 * A010467 A010468 A010469 KEYWORD nonn,cons AUTHOR STATUS approved

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Last modified July 11 14:30 EDT 2020. Contains 335626 sequences. (Running on oeis4.)