

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
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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 eightsmallest triangle with integer side lengths (2, 3, 3), or the seventhsmallest 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. 519523, 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 hth powers, J. Fac. Sci. Hokkaido Univ. Ser. I, 18, 124127, 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(12*i*sqrt(2)) = sqrt(1/2+2*i*sqrt(3)) + sqrt(1/22*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[8], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)


PROG

(PARI) { default(realprecision, 20080); x=sqrt(8); for (n=1, 20000, d=floor(x); x=(xd)*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

N. J. A. Sloane


STATUS

approved



