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A275056
Numerator of the alternating n-th partial sum of the reciprocals of the successive prime gaps.
2
1, 1, 1, 3, 5, 1, 3, 5, 17, 11, 13, 5, 4, 13, 5, 13, 19, 17, 5, 7, 4, 13, 5, 9, 11, 7, 9, 5, 7, 45, 59, 149, 233, 1081, 1501, 1361, 1501, 1291, 477, 1291, 1711, 1627, 2047, 1837, 2257, 729, 2257, 2047, 2467, 2257, 799, 659, 687, 1921, 687, 1921, 2341, 2201
OFFSET
1,4
LINKS
FORMULA
a(n) = Numerator(Sum_{i=1..n} ((-1)^(i - 1))/(prime(i+1)-prime(i))).
a(n) = Numerator(Sum_{i=1..n} ((-1)^(i - 1))/A001223(i)).
MATHEMATICA
Table[Numerator@Sum[((-1)^(j - 1))/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 120}];
Accumulate[Times@@@Partition[Riffle[1/Differences[Prime[Range[60]]], {1, -1}, {2, -1, 2}], 2]]//Numerator (* Harvey P. Dale, Jun 22 2021 *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Andres Cicuttin, Jul 14 2016
STATUS
approved