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 A051887 #27 Feb 25 2025 02:13:36
%S A051887 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 A051887 31,2,47,13,113,7,137,103,43,41,97,3,173,97,41,13,97,59,29,53,3,107,
%U A051887 127,197,3,487,433,31,281,587,7,89,41,47,193,239,41,7,31,67
%N A051887 Minimal and special 2k-Germain primes, where 2k is in A002110 (primorial numbers).
%C A051887 a(n) is the minimal prime p such that primorial(n)*p + 1 is also prime.
%C A051887 While p is in A005384, the primorial(n)*p + 1 primes are in A051902 (primorial-safe primes).
%C A051887 Analogous to or subset of A051686, where the even numbers are 2, 6, ..., A002110(n), ...
%H A051887 Amiram Eldar, <a href="/A051887/b051887.txt">Table of n, a(n) for n = 1..1000</a>
%F A051887 a(n) = (A051902(n)-1)/A002110(n). - _Amiram Eldar_, Feb 25 2025
%e A051887 a(25) = 47 because primorial(25)*47 + 1 is also prime and minimal with this property: primorial(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 A051887 Table[p = 2; While[! PrimeQ[Product[Prime@ i, {i, n}] p + 1], p = NextPrime@ p]; p, {n, 68}] (* _Michael De Vlieger_, Jun 29 2017 *)
%o A051887 (PARI) a(n) = {my(p = 2, r = vecprod(primes(n))); while(!isprime(p * r + 1), p = nextprime(p+1)); p;} \\ _Amiram Eldar_, Feb 25 2025
%Y A051887 Cf. A002110, A005384, A005385, A051686, A007693, A051886, A051888, A051902.
%K A051887 nonn
%O A051887 1,1
%A A051887 _Labos Elemer_, Dec 15 1999
%E A051887 More terms from _Michael De Vlieger_, Jun 29 2017