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Search: id:A059444
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| A059444 |
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Decimal expansion of square root of (Pi * e / 2). |
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+0
3
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| 2, 0, 6, 6, 3, 6, 5, 6, 7, 7, 0, 6, 1, 2, 4, 6, 4, 6, 9, 2, 3, 4, 6, 9, 5, 9, 4, 2, 1, 4, 9, 9, 2, 6, 3, 2, 4, 7, 2, 2, 7, 6, 0, 9, 5, 8, 4, 9, 5, 6, 5, 4, 2, 2, 5, 7, 7, 8, 3, 2, 5, 6, 2, 6, 8, 9, 8, 9, 7, 8, 9, 6, 4, 2, 5, 6, 7, 0, 8, 5, 1, 6, 1, 8, 1, 2, 6, 0, 1, 8, 1, 2, 2, 7, 7, 3, 3, 1, 4, 1
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Appears as constant factor in Proposition 1.12, p. 5, of Feige et al. (2007). - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 18 2007
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REFERENCES
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C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, Oxford and NY, 2001, page 68.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
Uri Feige, Guy Kindler, Ryan O Donnell, Understanding Parallel Repetition Requires Understanding Foams, Electronic Colloquium on Computational Complexity, Report TR07-043 (ISSN 1433-8092, 14th Year, 43rd Report), 7 May 2007.
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FORMULA
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Sqrt(Pi*e/2) = A + B with A = 1 + 1/(1*3) + 1/(1*3*5) + 1/(1*3*5*7) + 1/(1*3*5*7*9) + . . . = 1.410686134. . . (see A060196) and B = 1/(1 + 1/(1 + 2/(1 + 3/(1 + 4/(1 + 5/(1 + ...)))))) = 0.65567954241. . .- (S. Ramanujan)
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EXAMPLE
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2.066365677...
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MATHEMATICA
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RealDigits[N[Sqrt[ \[Pi]*\[ExponentialE]/2], 100]][[1]]
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PROGRAM
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(PARI) { default(realprecision, 20080); x=sqrt(Pi*exp(1)/2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b059444.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 27 2009]
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CROSSREFS
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Cf. A059445.
Adjacent sequences: A059441 A059442 A059443 this_sequence A059445 A059446 A059447
Sequence in context: A021488 A053206 A106848 this_sequence A057720 A087996 A086777
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KEYWORD
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nonn,cons,new
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 01 2001
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