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Search: id:A059956
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| A059956 |
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Decimal expansion of 6/Pi^2. |
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+0
12
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| 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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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"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.
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
In fact, the probability that any k randomly selected numbers will be coprimes is Sum {1..inf) 1/n^k. - rgwv
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REFERENCES
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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.
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LINKS
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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
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
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EXAMPLE
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.6079271018540266286632767792583658334261526480...
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MATHEMATICA
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RealDigits[ 6/Pi^2, 10, 105][[1]]
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PROGRAM
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(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)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 30 2009]
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CROSSREFS
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Equals 1/A013661. See A002117 for further references and links.
Sequence in context: A165071 A021900 A021626 this_sequence A011393 A066362 A083680
Adjacent sequences: A059953 A059954 A059955 this_sequence A059957 A059958 A059959
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KEYWORD
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easy,nonn,cons
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Mar 01 2001
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