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A274826
Denominator of the n-th partial sum of the reciprocals of the successive prime gaps.
2
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
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
KEYWORD
nonn,frac,look
AUTHOR
Andres Cicuttin, Jul 07 2016
STATUS
approved