A363585 Least prime p such that p^n + 6 is the product of n distinct primes.

5, 2, 23, 127, 71, 353, 1279, 3851, 3049, 18913, 47129, 352073, 696809

Offset: 1

Author

J.W.L. (Jan) Eerland, Jun 10 2023

Keywords

• nonn
• hard
• more

Comments

Corresponding values of p^n + 6 are 11, 10, 12173, 260144647, 1804229357, 1934854145598535, 5598785270206921122565, ...

Upper bounds for the next terms are a(12) <= 352073, a(13) <= 696809, a(14) <= 1496423. - Hugo Pfoertner, Jun 11 2023

Examples

			a(1) = 5; 5^1 + 6 = 11.
a(2) = 2; 2^2 + 6 = 2 * 5.
a(3) = 23; 23^3 + 6 = 7 * 37 * 47.
a(4) = 127; 127^4 + 6 = 7 * 131 * 367 * 773.
		

Crossrefs

Cf. A000961, A001221, A005117, A280005, A358656, A362957.

Programs

Mathematica

Table[b=6;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}]

PARI

a(n) = forprime(p=2, , my(f=factor(p^n + 6)); if (issquarefree(f) && (omega(f) == n), return(p)));

Extensions

a(11) from Hugo Pfoertner, Jun 11 2023

a(12) from J.W.L. (Jan) Eerland, Jan 07 2024

a(13) from Hugo Pfoertner, confirmed by Daniel Suteu, Feb 10 2024