Search: id:A059956
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%I A059956
%S A059956 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,
%T A059956 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,
%U A059956 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
%N A059956 Decimal expansion of 6/Pi^2.
%C A059956 "6/Pi^2 is the probability that two randomly selected numbers will be 
               coprime and also the probability that a randomly selected integer 
               is 'square-free.'" C. Pickover.
%C A059956 6/Pi^2=Product_{k=1..infinity} (1-1/ithprime(k)^2)=Sum_{k=1..infinity} 
               mu(k)/k^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 18 2001
%C A059956 In fact, the probability that any k randomly selected numbers will be 
               coprimes is Sum {1..inf) 1/n^k. - rgwv
%D A059956 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.
%D A059956 C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 
               359.
%H A059956 Harry J. Smith, <a href="b059956.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A059956 C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind 
               and Meaning," <a href="http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?first=1&maxdocs=3&type=html&an\
               =0983.00008&format=complete">Zentralblatt review</a>
%H A059956 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Hafner-Sarnak-McCurleyConstant.html">Hafner-Sarnak-McCurley Constant</
               a>
%H A059956 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RelativelyPrime.html">Relatively Prime</a>
%H A059956 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Squarefree.html">Squarefree</a>
%e A059956 .6079271018540266286632767792583658334261526480...
%t A059956 RealDigits[ 6/Pi^2, 10, 105][[1]]
%o A059956 (Harry J. Smith's VPcalc program): 150 M P x=6/Pi^2.
%o A059956 (PARI) { default(realprecision, 20080); x=60/Pi^2; for (n=0, 20000, d=floor(x); 
               x=(x-d)*10; write("b059956.txt", n, " ", d)); } [From Harry J. Smith 
               (hjsmithh(AT)sbcglobal.net), Jun 30 2009]
%Y A059956 Equals 1/A013661. See A002117 for further references and links.
%Y A059956 Sequence in context: A165071 A021900 A021626 this_sequence A011393 A066362 
               A083680
%Y A059956 Adjacent sequences: A059953 A059954 A059955 this_sequence A059957 A059958 
               A059959
%K A059956 easy,nonn,cons
%O A059956 0,1
%A A059956 Jason Earls (zevi_35711(AT)yahoo.com), Mar 01 2001

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