A129243 Least K such that K*(prime(n)^n)-1 is prime with prime(n)=n-th prime.

2, 2, 4, 2, 40, 6, 24, 14, 6, 14, 32, 54, 30, 108, 40, 110, 120, 182, 374, 20, 114, 2, 84, 80, 80, 110, 36, 78, 68, 200, 26, 228, 30, 12, 82, 294, 102, 530, 36, 98, 618, 2, 108, 734, 672, 404, 114, 458, 1102, 42, 154, 362, 998, 30, 58, 404, 28, 72, 434, 132, 266, 2, 308

Offset

1,1

Links

Table of n, a(n) for n=1..63.

Example

2*(2^1)-1=3 prime so a(1)=2;
2*(3^2)-1=17 prime so a(2)=2;
4*(5^3)-1=2499 prime so a(3)=4;
2*(7^4)-1=4801 prime so a(4)=2.

Mathematica

s={}; Do[k=0; Until[PrimeQ[k*Prime[n]^n-1], k++]; AppendTo[s, k], {n, 63}]; s (* James C. McMahon, Jan 17 2025 *)

Prog

(PARI) a(n) = {my(k=2, x=prime(n)^n); while (!isprime(k*x-1), k+=2); k; } \\ Michel Marcus, Sep 24 2019

Crossrefs

Cf. A129244, A129245.

Sequence in context: A227509 A279094 A299148 * A013551 A252040 A084896

Adjacent sequences: A129240 A129241 A129242 * A129244 A129245 A129246

Keyword

nonn

Author

Pierre CAMI, Apr 05 2007

Status

approved