cp's OEIS Frontend

A092065 Numbers m such that numerator of Sum_{k=1..m} 1/(prime(k)-k) is prime.

%I A092065 #31 Aug 27 2024 11:27:19
%S A092065 2,3,4,5,7,14,21,22,26,27,32,43,51,58,62,65,82,131,148,207,229,249,
%T A092065 257,320,334,386,423,440,481,747,823,1181,1314,1915,2025,2269,2700,
%U A092065 2717,2801,2865,4548,6015,6364,8532,10612,10863,11960,15156,15898,19186,19622,22203,25345
%N A092065 Numbers m such that numerator of Sum_{k=1..m} 1/(prime(k)-k) is prime.
%C A092065 Note that the definition here is subtly different from that of A092063.
%p A092065 count:= 0:
%p A092065 S:= 0: p:= 0;
%p A092065 for n from 1 to 2500 do
%p A092065   p:= nextprime(p);
%p A092065   S:= S + 1/(p - n);
%p A092065   if isprime(numer(S)) then
%p A092065     count:= count+1;
%p A092065     A[count]:= n;
%p A092065   fi
%p A092065 od:
%p A092065 seq(A[i],i=1..count); # _Robert Israel_, Sep 07 2014
%t A092065 f=0; Do[ p=Prime[n]; f=f+1/(p-n); g=Numerator[f]; If[ PrimeQ[g], Print[n]], {n,1,500} ]
%o A092065 (PARI) S=1;for(n=2,100,S=S+1/(prime(n)-n);if(isprime(numerator(S)),print1(n,","))) \\ _Edward Jiang_, Sep 08 2014
%Y A092065 Cf. A092066.
%K A092065 nonn
%O A092065 1,1
%A A092065 Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004; corrected Apr 24 2006
%E A092065 Sequence and Mathematica program corrected by _Alexander Adamchuk_, Jul 29 2007
%E A092065 a(30)-a(34) from _Vincenzo Librandi_, Nov 26 2012
%E A092065 a(35)-a(36) from _Robert Israel_, Sep 07 2014
%E A092065 a(37)-a(53) from _Michael S. Branicky_, Aug 26 2024