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Search: id:A053004
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| A053004 |
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Decimal expansion of M(1,sqrt(2)). |
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+0
4
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| 1, 1, 9, 8, 1, 4, 0, 2, 3, 4, 7, 3, 5, 5, 9, 2, 2, 0, 7, 4, 3, 9, 9, 2, 2, 4, 9, 2, 2, 8, 0, 3, 2, 3, 8, 7, 8, 2, 2, 7, 2, 1, 2, 6, 6, 3, 2, 1, 5, 6, 5, 1, 5, 5, 8, 2, 6, 3, 6, 7, 4, 9, 5, 2, 9, 4, 6, 4, 0, 5, 2, 1, 4, 1, 4, 3, 9, 1, 5, 6, 7, 0, 8, 3, 5, 8, 8, 5, 5, 5, 6, 4, 8, 9, 7, 9, 3, 3, 8, 9, 3, 7, 5, 9, 0
(list; cons; graph; listen)
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OFFSET
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1,3
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COMMENT
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M(a,b) is the limit of the arithmetic-geometric mean iteration applied repeatedly starting with a and b: a_0=a, b_0=b, a_{n+1}=(a_n+b_n)/2, b_{n+1}=sqrt(a_n*b_n).
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REFERENCES
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J. M. Borwein and P. B. Borwein, Pi and the AGM, page 5.
J. R. Goldman, The Queen of Mathematics, 1998, p. 92.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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1.19814023473559220743992249228...
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PROGRAM
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(PARI) { default(realprecision, 20080); x=agm(1, sqrt(2)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b053004.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 20 2009]
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CROSSREFS
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Cf. A014549, A053002, A053003.
Adjacent sequences: A053001 A053002 A053003 this_sequence A053005 A053006 A053007
Sequence in context: A021509 A021106 A072915 this_sequence A019888 A008570 A114864
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KEYWORD
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nonn,cons,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 21 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 22 2000
Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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