A103538 - OEIS

%I #14 May 29 2023 02:47:07

%S 1,2,3,5,6,7,13,16,20,23,64,191,490,3620,5909

%N Numbers k such that prime(k)*prime(k)# - 1 is prime, where prime(k)# is the k-th primorial.

%t q[n_] := PrimeQ[Prime[n]*Product[Prime[i], {i,1,n}] - 1]; Select[Range[500], q] (* _Amiram Eldar_, Jul 18 2021 *)

%t Module[{nn=500,p1,p2},p1=Prime[Range[nn]];p2=FoldList[Times,p1];Select[Thread[ {p1,p2}],PrimeQ[ Times@@#-1]&][[;;,1]]]//PrimePi (* _Harvey P. Dale_, May 21 2023 *)

%Y Cf. A002110.

%K nonn,more

%O 1,2

%A _Pierre CAMI_, Mar 22 2005

%E a(14) from _Amiram Eldar_, Jul 18 2021

%E a(15) from _Michael S. Branicky_, May 28 2023