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A274980
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Denominator of the alternating n-th partial sum of the reciprocals of the successive prime gaps.
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1
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1, 2, 1, 4, 4, 1, 2, 4, 12, 12, 12, 6, 3, 12, 4, 12, 12, 12, 3, 6, 3, 12, 4, 8, 8, 8, 8, 8, 8, 56, 56, 168, 168, 840, 840, 840, 840, 840, 280, 840, 840, 840, 840, 840, 840, 280, 840, 840, 840, 840, 280, 280, 280, 840, 280, 840, 840, 840, 840, 840, 168, 168, 168, 168, 168, 168, 168
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Denominator(Sum_{i=1..n} ((-1)^(i - 1))/(prime(i+1)-prime(i))).
a(n) = Denominator(Sum_{i=1..n} ((-1)^(i - 1))/A001223(i)).
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MATHEMATICA
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Table[Denominator@Sum[((-1)^(j - 1))/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 120}];
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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