

A059956


Decimal expansion of 6/Pi^2.


23



6, 0, 7, 9, 2, 7, 1, 0, 1, 8, 5, 4, 0, 2, 6, 6, 2, 8, 6, 6, 3, 2, 7, 6, 7, 7, 9, 2, 5, 8, 3, 6, 5, 8, 3, 3, 4, 2, 6, 1, 5, 2, 6, 4, 8, 0, 3, 3, 4, 7, 9, 2, 9, 3, 0, 7, 3, 6, 5, 4, 1, 9, 1, 3, 6, 5, 0, 3, 8, 7, 2, 5, 7, 7, 3, 4, 1, 2, 6, 4, 7, 1, 4, 7, 2, 5, 5, 6, 4, 3, 5, 5, 3, 7, 3, 1, 0, 2, 5, 6, 8, 1, 7, 3, 3
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OFFSET

0,1


COMMENTS

"6/Pi^2 is the probability that two randomly selected numbers will be coprime and also the probability that a randomly selected integer is 'squarefree.'" C. Pickover.
6/Pi^2 = Product_{k = 1..infinity} (11/ithprime(k)^2) = Sum_{k = 1..infinity} mu(k)/k^2.  Vladeta Jovovic, May 18 2001
In fact, the probability that any k randomly selected numbers will be coprimes is Sum {1..inf) 1/n^k.  Robert G. Wilson v
6/Pi^2 is also the diameter of a circle whose circumference equals the ratio of volume of a cuboid to the inscribed ellipsoid. 6/Pi^2 is also the diameter of a circle whose circumference equals the ratio of surface area of a cube to the inscribed sphere.  Omar E. Pol, Oct 08 2011
6/(Pi^2 * n^2) is the probability that two randomly selected positive integers will have a greatest common divisor equal to n, n >= 1.  Geoffrey Critzer, May 28 2013


REFERENCES

P. Diaconis and P. Erdos, On the distribution of the greatest common divisor, in A festschrift for Herman Rubin, pp. 5661, IMS Lecture Notes Monogr. Ser., 45, Inst. Math. Statist., Beachwood, OH, 2004.
C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 359.


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
H. J. Smith, XPCalc
Eric Weisstein's World of Mathematics, HafnerSarnakMcCurley Constant
Eric Weisstein's World of Mathematics, Relatively Prime
Eric Weisstein's World of Mathematics, Squarefree


EXAMPLE

.6079271018540266286632767792583658334261526480...


MAPLE

evalf(1/Zeta(2)) ; # R. J. Mathar, Mar 27 2013


MATHEMATICA

RealDigits[ 6/Pi^2, 10, 105][[1]]


PROG

(Harry J. Smith's VPcalc program): 150 M P x=6/Pi^2.
(PARI) { default(realprecision, 20080); x=60/Pi^2; for (n=0, 20000, d=floor(x); x=(xd)*10; write("b059956.txt", n, " ", d)); } \\ Harry J. Smith, Jun 30 2009


CROSSREFS

Equals 1/A013661. See A002117 for further references and links.
Sequence in context: A195432 A196915 A021626 * A201521 A011393 A066362
Adjacent sequences: A059953 A059954 A059955 * A059957 A059958 A059959


KEYWORD

easy,nonn,cons


AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Mar 01 2001


STATUS

approved



