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

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)]):
map(denom, R); # Robert Israel, Aug 02 2024

Mathematica

Table[Denominator@Sum[((-1)^(j - 1))/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 120}];

Crossrefs

Cf. A001223, A274828, A275056.

Sequence in context: A214670 A181878 A256791 * A274826 A129862 A137593

Adjacent sequences: A274977 A274978 A274979 * A274981 A274982 A274983

Keyword

nonn,frac,look

Author

Andres Cicuttin, Jul 14 2016

Status

approved