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A274827 Numerator of the n-th partial sum of the reciprocals of the successive prime gaps. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A246788 A342802 A099887 * A038220 A303901 A053151

Adjacent sequences:  A274824 A274825 A274826 * A274828 A274829 A274830

KEYWORD

nonn,frac,look

AUTHOR

Andres Cicuttin, Jul 07 2016

STATUS

approved

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Last modified May 14 03:00 EDT 2021. Contains 343872 sequences. (Running on oeis4.)