A274827 Numerator of the n-th partial sum of the reciprocals of the successive prime gaps.

1, 3, 2, 9, 11, 3, 7, 15, 47, 53, 55, 29, 16, 67, 23, 71, 77, 79, 41, 22, 15, 31, 95, 193, 199, 211, 217, 229, 235, 1657, 1699, 1727, 1811, 9139, 9559, 3233, 9839, 10049, 10189, 3443, 3583, 3611, 3751, 3821, 3961, 11953, 12023, 12233, 12653, 12863, 13003

Offset

1,2

Links

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

Formula

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

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

Maple

Primes:= select(isprime, [2, seq(i, i=3..10^4, 2)]):
map(numer, ListTools:-PartialSums(map(`^`, Primes[2..-1]-Primes[1..-2], -1))); # Robert Israel, Jul 26 2016

Mathematica

nmax=51; Table[Sum[1/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, nmax}]//Numerator;
Accumulate[1/Differences[Prime[Range[60]]]]//Numerator (* Harvey P. Dale, Dec 25 2017 *)

Prog

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

Crossrefs

Cf. A001223, A217538, A274826.

Sequence in context: A342802 A099887 A366348 * A038220 A303901 A053151

Adjacent sequences: A274824 A274825 A274826 * A274828 A274829 A274830

Keyword

nonn,frac,look

Author

Andres Cicuttin, Jul 07 2016

Status

approved