A358979 - OEIS

%I #48 Jan 24 2023 14:19:39

%S 3,19,11,29,131,631,983,353,9941,20089,15031,8387,102931

%N Least prime p such that p^n + 4 is the product of n distinct primes.

%C Corresponding values of p^n + 4 are 7, 365, 707285, 38579489655, 63121332085847285, 886899938586555644331, 241100240228887100165, ...

%C If they exist, a(14) > 106123, a(15) > 41257, a(16) > 31567.

%e a(1) = 3; 3^1 + 4 = 7.

%e a(2) = 19; 19^2 + 4 = 5 * 73.

%e a(3) = 11; 11^3 + 4 = 3 * 5 * 89.

%e a(4) = 29; 29^4 + 4 = 5 * 17 * 53 * 157.

%t Table[b=4;y[a_]:=FactorInteger[Prime[a]^n+b];k=1;Monitor[Parallelize[While[True,If[And[Length[y[k]]==n,Count[Flatten[y[k]],1]==n],Break[]];k++];k],k]//Prime,{n,1,10}]

%o (PARI) a(n) = forprime(p=2, , my(f=factor(p^n + 4)); if (issquarefree(f) && (omega(f) == n), return(p)));

%Y Cf. A358656, A280005, A000961, A005117.

%K nonn,more

%O 1,1

%A _J.W.L. (Jan) Eerland_, Dec 27 2022