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Search: id:A146481
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| A146481 |
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Decimal expansion of Product_{n=2...infinity} (1-1/(n*(n-1))). |
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1
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| 2, 9, 6, 6, 7, 5, 1, 3, 4, 7, 4, 3, 5, 9, 1, 0, 3, 4, 5, 7, 0, 1, 5, 5, 0, 2, 0, 2, 1, 9, 1, 4, 2, 8, 6, 4, 8, 6, 4, 8, 3, 1, 5, 1, 9, 1, 7, 8, 9, 4, 7, 8, 9, 0, 8, 1, 6
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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Product of Artin's constant A005596 and the equivalent almost-prime products.
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LINKS
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R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arXiv:0903.2514 [math.NT], first line Table 3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 28 2009]
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FORMULA
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The logarithm is -sum_{s>=2} sum_{j=1..floor[s/(1+r)]} binomial(s-r*j-1,j-1)*(1-Zeta(s))/j at r=1.
s*sum_{j=1..floor[s/2]} binomial(s-j-1,j-1)/j = A001610(s-1).
Equals 1/product_{k=1..2} Gamma(1-x_k) = -sin(A094886)/A000796, where x_k are the 2 roots of the polynomial x*(x+1)-1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009]
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EXAMPLE
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0.2966751347435910345.. = (1-1/2)*(1-1/6)*(1-1/12)*(1-1/20)*..
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MAPLE
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phi := (1+sqrt(5))/2; evalf(-sin(Pi*phi)/Pi) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009]
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CROSSREFS
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Cf. A005596.
Sequence in context: A010598 A152564 A138029 this_sequence A021341 A011247 A068632
Adjacent sequences: A146478 A146479 A146480 this_sequence A146482 A146483 A146484
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KEYWORD
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nonn,cons
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2009
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