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

Author

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

Keywords

• hard
• nonn

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

Examples

			1/(2-1) + 1/(3-1) = 3/2 and 3 is prime so a(1)=2.
		

Crossrefs

Cf. A092064, A120271.

Programs

Mathematica

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

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

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