A099228 Primes of the form m^k-k, with m and k > 1.

2, 5, 7, 23, 47, 61, 79, 167, 223, 359, 439, 503, 509, 727, 839, 997, 1019, 1087, 1223, 1367, 1847, 2207, 2399, 2741, 3023, 3719, 3967, 4093, 4759, 5039, 5623, 5927, 6553, 7919, 8179, 8647, 10607, 11447, 13687, 14159, 14639, 15619, 16127, 17159, 17573

Offset: 1

Author

T. D. Noe, Oct 06 2004

Keywords

• nonn

Comments

It appears that primes of this form are much more common than primes of the form m^k+k (A099227).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A057897 (numbers of the form m^k-k, with m and k > 1), A084746 (least k such that n^k-k is prime).

Cf. A099227.

Programs

Mathematica

nLim=32000; lst={}; Do[k=2; While[n=m^k-k; n<=nLim, AppendTo[lst, n]; k++ ], {m, 2, Sqrt[nLim]}]; Select[Union[lst], PrimeQ]