A275056 Numerator of the alternating n-th partial sum of the reciprocals of the successive prime gaps.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A274828, A001223, A274980.

Sequence in context: A130793 A243854 A084243 * A335960 A248916 A030311

Adjacent sequences: A275053 A275054 A275055 * A275057 A275058 A275059

Keyword

sign,frac

Author

Andres Cicuttin, Jul 14 2016

Status

approved