A111232 Least k such that k^prime(n) - k^((prime(n)+1)/2) + 1 is prime for n > 1.

2, 5, 2, 3, 5, 5, 9, 26, 9, 16, 11, 5, 6, 2, 46, 18, 16, 89, 10, 2, 2, 94, 7, 7, 16, 26, 230, 5, 2, 140, 34, 69, 114, 6, 2, 179, 994, 2, 76, 165, 8, 69, 3, 294, 230, 96, 7, 720, 684, 2029, 2, 2, 25, 135, 523, 271, 161, 1210, 139, 14, 34, 194, 238, 87, 355, 636, 40, 1114, 519, 2

Offset

2,1

Links

Table of n, a(n) for n=2..71.

Example

2^3 - 2^2 + 1 = 5, which is prime, so a(2) = 2.
2^5 - 2^3 + 1 = 25 = 5*5, and
3^5 - 3^3 + 1 = 217 = 7*31, but
5^5 - 5^3 + 1 = 3001, which is prime, so a(3) = 5.

Mathematica

seq={}; Do[k=1; Until[PrimeQ[k^Prime[n]-k^((Prime[n]+1)/2)+1], k++]; AppendTo[seq, k], {n, 2, 71}]; seq (* James C. McMahon, May 06 2024 *)

Prog

(PARI) a(n) = {my(k=1, p=prime(n)); while (!isprime(k^p-k^((p+1)/2)+1), k++); k; } \\ Michel Marcus, Sep 16 2019

Crossrefs

Sequence in context: A192885 A246904 A199611 * A087892 A078372 A154751

Adjacent sequences: A111229 A111230 A111231 * A111233 A111234 A111235

Keyword

nonn

Author

Pierre CAMI, Oct 28 2005

Extensions

a(33) and a(34) concatenated by Georg Fischer, Jun 22 2022

Status

approved