A074267 Primes of form p^n + k, where p is prime, n>1 and 0

5, 11, 17, 29, 53, 83, 127, 131, 173, 179, 181, 257, 293, 347, 349, 367, 373, 379, 541, 547, 853, 857, 859, 863, 967, 971, 977, 983, 991, 1373, 1381, 1399, 1693, 1697, 1699, 1709, 1721, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 2203, 2207, 2213, 2221, 2237

Offset: 1

Author

Reinhard Zumkeller, Sep 20 2002

Keywords

• nonn
• nice

Comments

The representation is not unique: a(7)=127=5^3+2=11^2+5.

A138363(A049084(a(n))) > 0.

Links

• R. Zumkeller, Table of n, a(n) for n = 1..1000

Programs

Mathematica

lst = {}; Do[q = p^n + k; If[ PrimeQ@p && PrimeQ@q, AppendTo[lst, q]], {p, 2, 50}, {k, p - 1}, {n, 2, Log[p, 3000]}]; Take[ Union@ lst, 49] (* Robert G. Wilson v, Sep 22 2007 *)