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A010503
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Decimal expansion of 1/sqrt(2).
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56
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7, 0, 7, 1, 0, 6, 7, 8, 1, 1, 8, 6, 5, 4, 7, 5, 2, 4, 4, 0, 0, 8, 4, 4, 3, 6, 2, 1, 0, 4, 8, 4, 9, 0, 3, 9, 2, 8, 4, 8, 3, 5, 9, 3, 7, 6, 8, 8, 4, 7, 4, 0, 3, 6, 5, 8, 8, 3, 3, 9, 8, 6, 8, 9, 9, 5, 3, 6, 6, 2, 3, 9, 2, 3, 1, 0, 5, 3, 5, 1, 9, 4, 2, 5, 1, 9, 3, 7, 6, 7, 1, 6, 3, 8, 2, 0, 7, 8, 6, 3, 6, 7, 5, 0, 6
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OFFSET
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0,1
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COMMENTS
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The decimal expansion of sqrt(50) = 5*sqrt(2) = 7.0710678118654752440... gives essentially the same sequence.
Also real and imaginary part of the square root of the imaginary unit. - Alonso del Arte, Jan 07 2011
1/sqrt(2) = (1/2)^(1/2) = (1/4)^(1/4) (see the comments in A072364).
If a triangle has sides whose lengths form a harmonic progression in the ratio 1 : 1/(1 + d) : 1/(1 + 2d) then the triangle inequality condition requires that d be in the range -1 + 1/sqrt(2) < d < 1/sqrt(2). - Frank M Jackson, Oct 11 2011
Let s_2(n) be the sum of the base-2 digits of n and epsilon(n) = (-1)^s_2(n), the Thue-Morse sequence A010060, then prod(n >= 0, ((2*n + 1)/(2*n + 2))^epsilon(n) ) = 1/sqrt(2). - Jonathan Vos Post, Jun 03 2012
The square root of 1/2 and thus it follows from the Pythagorean theorem that it is the sine of 45 degrees (and the cosine of 45 degrees). - Alonso del Arte, Sep 24 2012
Circumscribed sphere radius for a regular octahedron with unit edges. In electric engineering, ratio of effective amplitude to peak amplitude of an alternating current/voltage. - Stanislav Sykora, Feb 10 2014
Radius of midsphere (tangent to edges) in a cube with unit edges. - Stanislav Sykora, Mar 27 2014
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 0..20000
P. C. Fishburn and J. A. Reeds, Bell inequalities, Grothendieck's constant and root two, SIAM J. Discrete Math., Vol. 7, No. 1, Feb. 1994, pp 48-56.
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; arXiv:1108.6096 [math.NT], 2011, see p. 3 in the link.
Eric Weisstein's World of Mathematics, Digit Product.
Wikipedia, Platonic solid
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FORMULA
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1/sqrt(2) = cos(Pi/4) = sqrt(2)/2. - Eric Desbiaux, Nov 05 2008
a(n) = 9 - A268682(n). As constants, this sequence is 1 - A268682. - Philippe Deléham, Feb 21 2016
From Amiram Eldar, Jun 29 2020: (Start)
Equals sin(Pi/4) = cos(Pi/4).
Equals Integral_{x=0..Pi/4} cos(x) dx. (End)
Equals (1/2)*A019884 + A019824 * A010527 = A019851 * A019896 + A019812 * A019857. - R. J. Mathar, Jan 27 2021
Equals hypergeom([-1/2, -3/4], [5/4], -1). - Peter Bala, Mar 02 2022
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EXAMPLE
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0.7071067811865475...
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MAPLE
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Digits:=100; evalf(1/sqrt(2)); Wesley Ivan Hurt, Mar 27 2014
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MATHEMATICA
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N[ 1/Sqrt[2], 200]
RealDigits[1/Sqrt[2], 10, 120][[1]] (* Harvey P. Dale, Mar 25 2019 *)
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PROG
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(PARI) default(realprecision, 20080); x=10*(1/sqrt(2)); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b010503.txt", n, " ", d)); \\ Harry J. Smith, Jun 02 2009
(MAGMA) 1/Sqrt(2); // Vincenzo Librandi, Feb 21 2016
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CROSSREFS
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Cf. A040042, A072364, A268682.
Cf. A073084 (infinite tetration limit).
Platonic solids circumradii: A010527 (cube), A019881 (icosahedron), A179296 (dodecahedron), A187110 (tetrahedron).
Platonic solids midradii: A020765 (tetrahedron), A020761 (octahedron), A019863 (icosahedron), A239798 (dodecahedron).
Sequence in context: A036479 A085966 A010678 * A335727 A158857 A255727
Adjacent sequences: A010500 A010501 A010502 * A010504 A010505 A010506
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KEYWORD
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nonn,cons,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Harry J. Smith, Jun 02 2009
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STATUS
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approved
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