A348430 - OEIS

%I #14 Jan 29 2022 12:40:51

%S 3,5,17,107,215443,15017,1616617,19657257924643,8618654420263,

%T 3234846617,100280245067,3710369067407,

%U 19818939413097309267215847601753,102481630431415237,307444891294245707,320460058359035439847,961380175077106319537

%N a(n) is the least prime of the form x+2 where x is the product of n consecutive primes.

%H Robert Israel, <a href="/A348430/b348430.txt">Table of n, a(n) for n = 0..222</a>

%e a(4) = 17*19*23*29+2 because that is prime while 2*3*5*7+2, 3*5*7*11+2, ..., 13*17*19*23+2 are not.

%p f:= proc(n) local P, i, r;

%p   P:= mul(ithprime(i), i=2..n+1);

%p   for i from 2 do

%p     r:= P+2;

%p     if isprime(r) then return r fi;

%p     P:= P/ithprime(i)*ithprime(i+n);

%p   od

%p end proc:

%p map(f, [$0..20]);

%t a[n_] := Module[{x = Product[Prime[i], {i, 2, n + 1}], p1 = 3, p2 = Prime[n + 2]}, While[! PrimeQ[x + 2], x *= (p2/p1); p1 = NextPrime[p1]; p2 = NextPrime[p2]]; x + 2]; Array[a, 17, 0] (* _Amiram Eldar_, Jan 25 2022 *)

%Y Cf. A347866, A083562.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 25 2022