A092063 - OEIS

%I #18 Aug 26 2024 09:53:22

%S 2,3,4,7,8,15,19,21,22,25,26,31,34,45,46,52,65,69,79,85,89,98,102,122,

%T 137,149,181,195,210,220,316,325,340,385,436,466,497,934,972,1180,

%U 1211,1212,1639,1807,2075,2104,3100,3258,3563,3688,4528,4760,4934,6151,6185,7579,8625,8694,9205

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

%C Note that the definition here is subtly different from that of A092065.

%C 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

%C Intersection of A000040 (the primes) and A120271 (numerators of partial sums of 1/(prime(i)-1)). - _M. F. Hasler_, Feb 06 2008

%C a(60) > 10000. - _Jason Yuen_, Aug 26 2024

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

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

%o (PARI) A120271(n) = numerator(sum(k=1, n, 1/(prime(k)-1)));

%o for (i=1,500,if(isprime(A120271(i)),print1(i,",")));

%o (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

%Y Cf. A092064, A120271.

%K hard,nonn

%O 1,1

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

%E More terms from _M. F. Hasler_, Feb 06 2008

%E Edited by _T. D. Noe_, Oct 30 2008

%E Corrected by _Harvey P. Dale_, Oct 16 2016

%E a(48)-a(59) from _Jason Yuen_, Aug 26 2024