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A274826
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Denominator of the n-th partial sum of the reciprocals of the successive prime gaps.
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2
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1, 2, 1, 4, 4, 1, 2, 4, 12, 12, 12, 6, 3, 12, 4, 12, 12, 12, 6, 3, 2, 4, 12, 24, 24, 24, 24, 24, 24, 168, 168, 168, 168, 840, 840, 280, 840, 840, 840, 280, 280, 280, 280, 280, 280, 840, 840, 840, 840, 840, 840, 840, 840, 280, 840, 840, 840, 280, 280, 280, 280, 280, 280, 280
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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/(prime(i+1)-prime(i)).
a(n) = Denominator(Sum_{i=1..n} 1/A001223(i)).
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MAPLE
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G:= [seq(1/(ithprime(n+1)-ithprime(n)), n=1..100)]:
L:= ListTools:-PartialSums(G):
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MATHEMATICA
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nmax=64; Table[Sum[1/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, nmax}]//Denominator;
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PROG
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(PARI) a(n) = denominator(sum(i=1, n, 1/(prime(i+1)-prime(i)))) \\ Felix Fröhlich, Jul 07 2016
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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