A351848 - OEIS

%I #5 Feb 23 2022 09:21:30

%S 3,7,423281,0

%N a(n) is the least prime p such that k*(p^2-1)+2*n+1 is prime for k=1..2*n, or 0 if there is no such p.

%C If n == 1 (mod 3) and n > 1, then a(n) = 0.

%C a(5) > 10^10 if it is not 0.

%e a(2) = 7 because 5 + 1*(7^2-1) = 53, 5 + 2*(7^2-1) = 101, 5 + 3*(7^2-1) = 149 and 5 + 4*(7^2-1) = 197 are all prime.

%p f:= proc(n) local p,pmax,k;

%p   if n mod 3 = 1 then

%p     if n=1 then return 3 else return 0 fi

%p   fi;

%p   p:= 1:

%p   while p < 10^8 do

%p     p:= nextprime(p);

%p     if andmap(isprime, [seq(k*(p^2-1)+2*n+1, k=1..2*n)]) then return p fi

%p   od;

%p FAIL

%p end proc:

%p map(f, [$1..5]);

%K nonn,more

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 21 2022