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A340468 a(n) is the least prime of the form 2 + Product_{i=n..m} prime(i).

%I A340468 #13 Jan 11 2021 10:51:03
%S A340468 5,7,79,13,223,19,439,
%T A340468 130753887906569681111538991218568790437537693430279000532630035672131604633987039552816424896353327834998483765849409837393409377729040653460715050958787058270805333463,
%U A340468 31,34826927179023475480751694965449235272424989980919
%N A340468 a(n) is the least prime of the form 2 + Product_{i=n..m} prime(i).
%C A340468 If n is in A029707, a(n) = 2+prime(n).
%C A340468 If n is not in A029707 but prime(n) is in A051507, a(n) = 2+prime(n)*prime(n+1).
%C A340468 a(15) > 10^1000 if it exists.
%H A340468 Robert Israel, <a href="/A340468/b340468.txt">Table of n, a(n) for n = 2..14</a>
%e A340468 a(2) = 2+3 = 5.
%e A340468 a(3) = 2+5 = 7.
%e A340468 a(4) = 2+7*11 = 79.
%e A340468 a(5) = 2+11 = 13.
%e A340468 a(6) = 2+13*17 = 223.
%e A340468 a(7) = 2+17 = 19.
%e A340468 a(8) = 2+19*23 = 439.
%e A340468 a(9) = 2+23*29*...*431.
%p A340468 f:= proc(n) local i,t;
%p A340468   t:= 1;
%p A340468   for i from n do
%p A340468     t:= t*ithprime(i);
%p A340468     if isprime(t+2) then return t+2 fi;
%p A340468   od
%p A340468 end proc:
%p A340468 seq(f(n),n=2..14);
%o A340468 (Python)
%o A340468 from sympy import isprime, nextprime, prime
%o A340468 def a(n):
%o A340468   prodpnpm = pm = prime(n)
%o A340468   while not isprime(2+prodpnpm): pm = nextprime(pm); prodpnpm *= pm
%o A340468   return 2+prodpnpm
%o A340468 print([a(n) for n in range(2, 12)]) # _Michael S. Branicky_, Jan 08 2021
%Y A340468 Cf. A029707, A051507.
%K A340468 nonn
%O A340468 2,1
%A A340468 _Robert Israel_, Jan 08 2021