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Search: id:A125684
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| 3, 4, 5, 6, 7, 8, 10, 13, 14, 18, 21, 22, 26, 27, 28, 32, 33, 35, 51, 54, 58, 67, 76, 89, 100, 140, 170, 189, 269, 307, 365, 408, 470, 475, 546, 558, 604, 751, 771, 857, 892, 896, 992, 1031, 1080, 1181, 1228, 1289, 1342
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OFFSET
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1,1
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COMMENT
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A125683(n) = Numerator[ Sum[ (-1)^(k+1) * 1/(k(k+1)), {k,1,n} ]. Corresponding primes are listed in A125685(n) = A125683[ a(n) ] = {5,11,2,79,331,479,5297,70061,69203,8960447,45083347,...}.
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EXAMPLE
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A125683(n) begins {1,1,5,11,2,79,331,479,493,5297,2701,69071,70061,...}.
Thus a(1) = 3 because A125683(3) = 5 is prime but A125683(k) is not prime for k<3.
a(2)-a(6) = {4,5,6,7,8} because A125683(k) is prime for 3<k<9.
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MATHEMATICA
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g=0; Do[g=g+(-1)^(n+1)*1/(n(n+1)); f=Numerator[g]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 1342}]
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CROSSREFS
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Cf. A125683, A125685.
Sequence in context: A039078 A073632 A066378 this_sequence A089358 A001272 A047563
Adjacent sequences: A125681 A125682 A125683 this_sequence A125685 A125686 A125687
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 30 2006
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