|
| |
|
|
A010503
|
|
Decimal expansion of 1/sqrt(2).
|
|
15
| |
|
|
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
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
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 [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 05 2008]
Also real and imaginary part of the square root of the imaginary unit. [From Alonso del Arte (alonso.delarte(AT)gmail.com), 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 an 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
|
|
|
LINKS
| Harry J. Smith, Table of n, a(n) for n=0..20000
Bell inequalities, Grothendieck's constant and root two [From Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 05 2008]
J. Sondow and D. Marques, Algebraic and transcendental solutions of some exponential equations, Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 3 in the link.
|
|
|
EXAMPLE
| 0.7071067811865475...
|
|
|
MATHEMATICA
| N[ 1/Sqrt[2], 200]
|
|
|
PROG
| (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)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009]
|
|
|
CROSSREFS
| Cf. A040042, A072364.
Sequence in context: A036479 A085966 A010678 * A158857 A011438 A202996
Adjacent sequences: A010500 A010501 A010502 * A010504 A010505 A010506
|
|
|
KEYWORD
| nonn,cons,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Added more terms. Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 02 2009
|
| |
|
|
