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Search: id:A146485
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| A146485 |
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Decimal expansion of Product_{n=2...infinity} (1-1/(n^2*(n-1))). |
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1
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| 6, 7, 3, 9, 1, 7, 3, 6, 3, 3, 7, 6, 3, 5, 7, 5, 4, 1, 6, 6, 4, 4, 0, 8, 9, 7, 9, 3, 2, 2, 6, 3, 4, 4, 3, 8, 5, 6, 4, 7, 5, 9, 8, 1, 2, 3, 1, 2, 6, 7, 1, 7, 3, 6, 7, 9, 2
(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 of rank 2 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], table 3, first line with r=2. [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=2.
s*sum_{j=1..floor[s/3]} binomial(s-2j-1,j-1)/j = A001609(s)-1.
Equals 1/product_{k=1..3} Gamma(1-x_k), where x_k are the 3 roots of the polynomial x*(x+1)^2-1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009]
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EXAMPLE
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0.6739173633763... = (1-1/4)*(1-1/18)*(1-1/48)*(1-1/100)*...
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MAPLE
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r := 2 : ni := fsolve( (n+1)^r*n-1, n, complex) : 1.0/mul(GAMMA(1-d), d=ni) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 20 2009]
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CROSSREFS
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Cf. A065414.
Sequence in context: A139350 A092560 A018248 this_sequence A049254 A144028 A089321
Adjacent sequences: A146482 A146483 A146484 this_sequence A146486 A146487 A146488
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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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