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A010466 Decimal expansion of square root of 8. 28
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

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

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[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=(x-d)*10; write("b010466.txt", n, " ", d)); } \\ Harry J. Smith, Jun 02 2009

CROSSREFS

Cf. A040005 (continued fraction).

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

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Last modified June 25 09:38 EDT 2017. Contains 288709 sequences.