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A274980

Denominator of the alternating n-th partial sum of the reciprocals of the successive prime gaps.

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

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

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)).

MAPLE

P:= [seq(ithprime(i), i=1..101)]:

G:= P[2..-1]-P[1..-2]:

R:= ListTools:-PartialSums([seq((-1)^i/G[i], i=1..100)]):