A391385 a(n) is the smallest number k > 1 such that k^(2^m) + 1 is prime for all m = 1 to n, but not for m=n+1.

10, 6, 4, 2, 2090676

Offset

1,1

Links

Table of n, a(n) for n=1..5.

Mathematica

a[n_]:=Module[{k=2}, While[!AllTrue[Table[k^(2^i)+1, {i, n}], PrimeQ]||PrimeQ[k^(2^(n+1))+1], k++]; k]; Array[a, 5] (* Stefano Spezia, Dec 08 2025 *)

Prog

(PARI) isok(k, n) = for (i=1, n, if (!ispseudoprime(k^(2^i) + 1), return(0))); return(!ispseudoprime(k^(2^(n+1)) + 1));
a(n) = my(k=2); while (!isok(k, n), k++); k;

Crossrefs

Cf. A389254 (where k^(2^(n+1)) + 1 can be prime).

Sequence in context: A370388 A010171 A006518 * A094175 A383169 A193952

Adjacent sequences: A391382 A391383 A391384 * A391386 A391387 A391388

Keyword

nonn,more

Author

Michel Marcus, Dec 08 2025

Status

approved