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%I #17 Nov 20 2017 03:28:53
%S 2,2,2,2,2,5,17,11,11,11,2,23,7,43,19,3,5,2,7,3,61,53,2,41,47,2,5,7,
%T 31,2,47,13,113,7,137,103,43,41,97,3,173,97,41,13,97,59,29,53,3,107,
%U 127,197,3,487,433,31,281,587,7,89,41,47,193,239,41,7,31,67
%N Minimal and special 2k-Germain primes, where 2k is in A002110 (primorial numbers).
%C Minimal p sequence such that primorial*p + 1 is also prime.
%C While p is in A005384, the Q(n)p + 1 primes are in A005385(primorial-safe primes).
%F Analogous to or subset of A051686, where the even numbers are 2, 6, ..., A002110(n), ...
%e a(25) is 47 because Q(25)*47 + 1 is also prime and minimal with this property: Q(25)*47 + 1 = 47*2305567963945518424753102147331756070 + 1 = 108361694305439365963395800924592535291 is a minimal prime. The first 6 terms (2,2,2,2,2,5) correspond to first entries in A005384, A007693, A051645, A051647, A051653, A051654 respectively.
%t Table[p = 2; While[! PrimeQ[Product[Prime@ i, {i, n}] p + 1], p = NextPrime@ p]; p, {n, 68}] (* _Michael De Vlieger_, Jun 29 2017 *)
%Y Cf. A002110, A005384, A005385, A051686, A007693, A051886, A051888.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 15 1999
%E More terms from _Michael De Vlieger_, Jun 29 2017