A274826 Denominator of the 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, 6, 3, 2, 4, 12, 24, 24, 24, 24, 24, 24, 168, 168, 168, 168, 840, 840, 280, 840, 840, 840, 280, 280, 280, 280, 280, 280, 840, 840, 840, 840, 840, 840, 840, 840, 280, 840, 840, 840, 280, 280, 280, 280, 280, 280, 280

Offset

1,2

Links

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

Formula

a(n) = Denominator(Sum_{i=1..n} 1/(prime(i+1)-prime(i)).

a(n) = Denominator(Sum_{i=1..n} 1/A001223(i)).

Maple

G:= [seq(1/(ithprime(n+1)-ithprime(n)), n=1..100)]:
L:= ListTools:-PartialSums(G):
map(denom, L); # Robert Israel, Jan 22 2020

Mathematica

nmax=64; Table[Sum[1/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, nmax}]//Denominator;

Prog

(PARI) a(n) = denominator(sum(i=1, n, 1/(prime(i+1)-prime(i)))) \\ Felix Fröhlich, Jul 07 2016

Crossrefs

Cf. A001223, A217538, A274827.

Sequence in context: A181878 A256791 A274980 * A129862 A137593 A009949

Adjacent sequences: A274823 A274824 A274825 * A274827 A274828 A274829

Keyword

nonn,frac,look

Author

Andres Cicuttin, Jul 07 2016

Status

approved