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A059956 Decimal expansion of 6/Pi^2. 25
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 (list; constant; graph; refs; listen; history; text; internal format)
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} (1-1/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. 56-61, 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, Hafner-Sarnak-McCurley 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=(x-d)*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 * A245700 A201521 A011393

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

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Last modified October 20 06:03 EDT 2014. Contains 248329 sequences.