This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109628 #23 Sep 16 2024 12:01:00
%S A109628 2,3,5,6,18,19,22,47,57,58,63,70,73,112,632,1382,4621
%N A109628 Numbers k such that the numerator of Sum_{i=1..k} 1/prime(i), in reduced form, is prime.
%C A109628 Terms <= 112 correspond to certified primes.
%C A109628 Numbers k such that the arithmetic derivative of the k-th primorial, A024451(k) [= A003415(A002110(k))] is prime. - _Antti Karttunen_, Jan 09 2024
%e A109628 Sum_{i=1..6} 1/prime(i) = 40361/30030 and 40361 is prime, hence 6 is a term.
%t A109628 s = 0; Do[s += 1/Prime[n]; k = Numerator[s]; If[PrimeQ[k], Print[n]], {n, 1, 1500}]
%t A109628 Position[Accumulate[1/Prime[Range[120]]],_?(PrimeQ[ Numerator[ #]]&)] //Flatten (* To generate terms greater than 120, increase the Range constant, but the program may take much longer to run. *) (* _Harvey P. Dale_, Jan 01 2019 *)
%Y A109628 Cf. A002110, A003415.
%Y A109628 Positions of primes in A024451.
%K A109628 hard,more,nonn
%O A109628 1,1
%A A109628 _Ryan Propper_, Aug 02 2005
%E A109628 a(17) from _Michael S. Branicky_, Sep 16 2024