A109628 Numbers k such that the numerator of Sum_{i=1..k} 1/prime(i), in reduced form, is prime.

2, 3, 5, 6, 18, 19, 22, 47, 57, 58, 63, 70, 73, 112, 632, 1382, 4621

Offset: 1

Author

Ryan Propper, Aug 02 2005

Keywords

• hard
• more
• nonn

Comments

Terms <= 112 correspond to certified primes.

Numbers k such that the arithmetic derivative of the k-th primorial, A024451(k) [= A003415(A002110(k))] is prime. - Antti Karttunen, Jan 09 2024

Examples

			Sum_{i=1..6} 1/prime(i) = 40361/30030 and 40361 is prime, hence 6 is a term.
		

Crossrefs

Cf. A002110, A003415.

Positions of primes in A024451.

Programs

Mathematica

s = 0; Do[s += 1/Prime[n]; k = Numerator[s]; If[PrimeQ[k], Print[n]], {n, 1, 1500}]
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 *)

Extensions

a(17) from Michael S. Branicky, Sep 16 2024