

A092063


Numbers n such that numerator of Sum_{i=1..n} 1/(prime(i)1) is prime.


6



2, 3, 4, 7, 8, 15, 19, 21, 22, 25, 26, 31, 34, 45, 46, 52, 65, 69, 79, 85, 89, 98, 102, 122, 137, 149, 181, 195, 210, 220, 316, 325, 340, 385, 436, 466, 497, 934, 972, 1180, 1211, 1212, 1639, 1807, 2075, 2104, 3100
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OFFSET

1,1


COMMENTS

Note that the definition here is subtly different from that of A092065.
Terms a(k) < 1000 correspond to primes. Beyond, numerators are probable primes. Note that A120271(3100) has 2187 digits.  M. F. Hasler, Feb 06 2008
Intersection of A000040 (the primes) and A120271 (numerators of partial sums of 1/(prime(i)1)).  M. F. Hasler, Feb 06 2008


LINKS

Table of n, a(n) for n=1..47.


EXAMPLE

1/(21) + 1/(31) = 3/2 and 3 is prime so a(1)=2


MATHEMATICA

Position[Accumulate[1/(Prime[Range[3100]]1)], _?(PrimeQ[ Numerator[ #]]&)]//Flatten (* Harvey P. Dale, Oct 16 2016 *)


PROG

(PARI) f(n)= s=0; for(i=1, n, s=s+1/(prime(i)1)); return(s); for (i=1, 500, if(isprime(numerator(f(i))), print1(i, ", ")));
(PARI) print_A092063( i=0 /* start testing at i+1 */)={local(s=sum(j=1, i, 1/(prime(j)1))); while(1, while(!ispseudoprime(numerator(s+=1/(prime(i++)1))), ); print1(i", "))}  M. F. Hasler, Feb 06 2008


CROSSREFS

Cf. A092064, A120271.
Sequence in context: A116961 A300486 A120611 * A227007 A126850 A007497
Adjacent sequences: A092060 A092061 A092062 * A092064 A092065 A092066


KEYWORD

hard,nonn


AUTHOR

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004


EXTENSIONS

More terms from M. F. Hasler, Feb 06 2008
Edited by T. D. Noe, Oct 30 2008
Corrected by Harvey P. Dale, Oct 16 2016


STATUS

approved



