A118377 - OEIS

%I #10 Sep 11 2021 10:47:34

%S 2,2,2,2,3,3,2,2,13,3,13,2,3,11,7,37,151,11,113,2,5,2,401,73,7,109,3,

%T 7,101,2,11,109,5,277,11,7,31,89,191,31,11,2713,11,13,73,461,17,17,5,

%U 41,257,17,127,1307,53,71,281,829,139,269,137,7,41,19,107,89

%N a(n) is the least prime p such that prime(n)# * p# - 1 is prime.

%e 2*2-1 = 3 is prime, 2 = p(1)#, so a(1) = 2.

%e 2*3*2-1 = 11 is prime, 2*3 = p(2)#, so a(2) = 2.

%e 2*3*5*2-1 = 59 is prime, 2*3*5 = p(3)#, so a(3) = 2.

%e 2*3*5*7*2-1 = 419 is prime, 2*3*5*7 = p(4)#, so a(4) = 2.

%e 2*3*5*7*11*2*3-1 = 13859 is prime, 2*3*5*7*11 = p(5)#, so a(5) = 3.

%t pr[n_] := Product[Prime[i], {i,1,n}]; a[n_] := Module[{prn = pr[n], k = 1}, While[!PrimeQ[prn*pr[k] - 1], k++]; Prime[k]]; Array[a, 50] (* _Amiram Eldar_, Sep 11 2021 *)

%o (PARI) pr(p) = my(pr=1); forprime(q=2, p, pr *= q); pr;

%o a(n) = my(p=2, P=pr(prime(n))); while (!ispseudoprime(P*pr(p)-1), p = nextprime(p+1)); p; \\ _Michel Marcus_, Sep 11 2021

%Y Cf. A002110.

%K nonn

%O 1,1

%A _Pierre CAMI_, May 15 2006

%E More terms from _Amiram Eldar_, Sep 11 2021