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%I #15 Jun 26 2021 01:59:41
%S 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,
%T 45,59,149,233,1081,1501,1361,1501,1291,477,1291,1711,1627,2047,1837,
%U 2257,729,2257,2047,2467,2257,799,659,687,1921,687,1921,2341,2201
%N Numerator of the alternating n-th partial sum of the reciprocals of the successive prime gaps.
%H Harvey P. Dale, <a href="/A275056/b275056.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Numerator(Sum_{i=1..n} ((-1)^(i - 1))/(prime(i+1)-prime(i))).
%F a(n) = Numerator(Sum_{i=1..n} ((-1)^(i - 1))/A001223(i)).
%t Table[Numerator@Sum[((-1)^(j - 1))/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 120}];
%t Accumulate[Times@@@Partition[Riffle[1/Differences[Prime[Range[60]]],{1,-1},{2,-1,2}],2]]//Numerator (* _Harvey P. Dale_, Jun 22 2021 *)
%Y Cf. A274828, A001223, A274980.
%K sign,frac
%O 1,4
%A _Andres Cicuttin_, Jul 14 2016