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A154920
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Denominators of a ternary BBP-type formula for ln(3)
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7
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1, 18, 27, 324, 405, 4374, 5103, 52488, 59049, 590490, 649539, 6377292, 6908733, 66961566, 71744535, 688747536, 731794257, 6973568802, 7360989291, 69735688020, 73222472421, 690383311398, 721764371007, 6778308875544
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OFFSET
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0,2
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COMMENTS
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ln(3) = sum(k>=0, {9/(2k+1)+1/(2k+2)}/9^(k+1) )
ln(3) = 1 + sum(k>=0, {1/(2k+2)+1/(2k+3)}/9^(k+1) )
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LINKS
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Table of n, a(n) for n=0..23.
David H. Bailey, A Compendium of BBP-Type Formulas for Mathematical Constants, page 14. [From Jaume Oliver Lafont, Sep 25 2009]
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FORMULA
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a(n)=(n+1)*9^[(n+1)/2]=18*a(n-2)-81*a(n-4)
sum(n>=0,1/a(n))=ln(3)
G.f.: (1+18*x+9*x^2)/(1-9*x^2)^2 [From Jaume Oliver Lafont, Jan 29 2009]
a(n)=(2-(-1)^n)*(n+1)*3^n [From Jaume Oliver Lafont, Sep 27 2009]
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PROG
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(PARI) a(n)=(n+1)*9^((n+1)\2) [From Jaume Oliver Lafont, Mar 25 2009]
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CROSSREFS
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Cf. A002391,A058962.
Cf. A164985, A165132. [From Jaume Oliver Lafont, Sep 25 2009]
Sequence in context: A038632 A138336 A166630 * A094224 A128858 A141782
Adjacent sequences: A154917 A154918 A154919 * A154921 A154922 A154923
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KEYWORD
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nonn
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AUTHOR
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Jaume Oliver Lafont, Jan 17 2009, Jan 18 2009
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STATUS
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approved
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