

A010503


Decimal expansion of 1/sqrt(2).


52



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

0,1


COMMENTS

The decimal expansion of sqrt(50) = 5*sqrt(2) = 7.0710678118654752440... gives essentially the same sequence.
1/sqrt(2) = cos(Pi/4) = sqrt(2)/2.  Eric Desbiaux, Nov 05 2008
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 base2 digits of n and epsilon(n) = (1)^s_2(n), the ThueMorse 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


LINKS

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 4856.
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151164; arXiv:1108.6096 [math.NT], 2011, see p. 3 in the link.
Eric Weisstein's World of Mathematics, Digit Product.
Wikipedia, Platonic solid


FORMULA

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)


EXAMPLE

0.7071067811865475...


MAPLE

Digits:=100; evalf(1/sqrt(2)); Wesley Ivan Hurt, Mar 27 2014


MATHEMATICA

N[ 1/Sqrt[2], 200]
RealDigits[1/Sqrt[2], 10, 120][[1]] (* Harvey P. Dale, Mar 25 2019 *)


PROG

(PARI) default(realprecision, 20080); x=10*(1/sqrt(2)); for (n=0, 20000, d=floor(x); x=(xd)*10; write("b010503.txt", n, " ", d)); \\ Harry J. Smith, Jun 02 2009
(MAGMA) 1/Sqrt(2); // Vincenzo Librandi, Feb 21 2016


CROSSREFS

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


KEYWORD

nonn,cons,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Harry J. Smith, Jun 02 2009


STATUS

approved



