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

1,1

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

Links

Table of n, a(n) for n=1..13.

Example

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.

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}]

Prog

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

Crossrefs

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

Sequence in context: A367675 A372063 A230416 * A034079 A090882 A191702

Adjacent sequences: A363582 A363583 A363584 * A363586 A363587 A363588

Keyword

nonn,hard,more

Author

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

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

Status

approved