A092063 Numbers k such that numerator of Sum_{i=1..k} 1/(prime(i)-1) is prime.

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, 3258, 3563, 3688, 4528, 4760, 4934, 6151, 6185, 7579, 8625, 8694, 9205

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

a(60) > 10000. - Jason Yuen, Aug 26 2024

Links

Table of n, a(n) for n=1..59.

Example

1/(2-1) + 1/(3-1) = 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) A120271(n) = numerator(sum(k=1, n, 1/(prime(k)-1)));
for (i=1, 500, if(isprime(A120271(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 A370858 A126850

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

a(48)-a(59) from Jason Yuen, Aug 26 2024

Status

approved