cp's OEIS Frontend

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

%I A092063 #18 Aug 26 2024 09:53:22
%S A092063 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 A092063 137,149,181,195,210,220,316,325,340,385,436,466,497,934,972,1180,
%U A092063 1211,1212,1639,1807,2075,2104,3100,3258,3563,3688,4528,4760,4934,6151,6185,7579,8625,8694,9205
%N A092063 Numbers k such that numerator of Sum_{i=1..k} 1/(prime(i)-1) is prime.
%C A092063 Note that the definition here is subtly different from that of A092065.
%C A092063 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 A092063 Intersection of A000040 (the primes) and A120271 (numerators of partial sums of 1/(prime(i)-1)). - _M. F. Hasler_, Feb 06 2008
%C A092063 a(60) > 10000. - _Jason Yuen_, Aug 26 2024
%e A092063 1/(2-1) + 1/(3-1) = 3/2 and 3 is prime so a(1)=2.
%t A092063 Position[Accumulate[1/(Prime[Range[3100]]-1)],_?(PrimeQ[ Numerator[ #]]&)]//Flatten (* _Harvey P. Dale_, Oct 16 2016 *)
%o A092063 (PARI) A120271(n) = numerator(sum(k=1, n, 1/(prime(k)-1)));
%o A092063 for (i=1,500,if(isprime(A120271(i)),print1(i,",")));
%o A092063 (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 A092063 Cf. A092064, A120271.
%K A092063 hard,nonn
%O A092063 1,1
%A A092063 Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004
%E A092063 More terms from _M. F. Hasler_, Feb 06 2008
%E A092063 Edited by _T. D. Noe_, Oct 30 2008
%E A092063 Corrected by _Harvey P. Dale_, Oct 16 2016
%E A092063 a(48)-a(59) from _Jason Yuen_, Aug 26 2024