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A065463
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Decimal expansion of product(1 - 1/(p*(p+1))), p prime >= 2).
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8
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7, 0, 4, 4, 4, 2, 2, 0, 0, 9, 9, 9, 1, 6, 5, 5, 9, 2, 7, 3, 6, 6, 0, 3, 3, 5, 0, 3, 2, 6, 6, 3, 7, 2, 1, 0, 1, 8, 8, 5, 8, 6, 4, 3, 1, 4, 1, 7, 0, 9, 8, 0, 4, 9, 4, 1, 4, 2, 2, 6, 8, 4, 2, 5, 9, 1, 0, 9, 7, 0, 5, 6, 6, 8, 2, 0, 0, 6, 7, 7, 8, 5, 3, 6, 8, 0, 8, 2, 4, 4, 1, 4, 5, 6, 9, 3, 1, 3
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OFFSET
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0,1
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COMMENTS
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The density of A268335. - Vladimir Shevelev, Feb 01 2016
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REFERENCES
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Laszlo Tóth, Alternating sums concerning multiplicative arithmetic functions, arXiv preprint arXiv:1608.00795, 2016
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LINKS
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Table of n, a(n) for n=0..97.
D. Handelman, Invariants for critical dimension groups and permutation-Hermite equivalence, arXiv preprint arXiv:1309.7417 [math.AC], 2013.
R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arxiv:0903.2514 [math.NT] (2009) constant Q_1^(1).
G. Niklasch, Some number theoretical constants: 1000-digit values
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
D. Zhang, W. Zhai, Mean Values of a Gcd-Sum Function Over Regular Integers Modulo n, J. Int. Seq. 13 (2010), 10.4.7, eq (4).
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EXAMPLE
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0.7044422009991655927366033503...
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MATHEMATICA
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$MaxExtraPrecision = 1200; digits = 98; terms = 1200; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0}, LinearRecurrence[{-2, 0, 1}, {-2, 3, -6}, terms + 10]]; r[n_Integer] := LR[[n]]; Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 18 2016 *)
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CROSSREFS
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Cf. A065490, A078082.
Sequence in context: A021146 A201424 A070513 * A242780 A011392 A177156
Adjacent sequences: A065460 A065461 A065462 * A065464 A065465 A065466
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KEYWORD
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cons,nonn
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AUTHOR
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N. J. A. Sloane, Nov 19 2001
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STATUS
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approved
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