A075073 Numbers k such that k-th perfect power - k is prime: A001597(k) - k is prime.

2, 3, 4, 5, 6, 11, 14, 17, 18, 23, 26, 35, 48, 50, 51, 76, 90, 92, 94, 124, 143, 145, 158, 159, 172, 173, 176, 177, 197, 230, 233, 254, 276, 317, 323, 333, 335, 352, 354, 355, 356, 386, 389, 405, 431, 440, 459, 472, 475, 480, 488

Offset: 1

Author

Zak Seidov, Oct 11 2002

Keywords

• easy
• nonn

Examples

			k=3: pp(3)-3 = 8-3 = 5 is prime.
		

Crossrefs

Cf. A001597.

Programs

Mathematica

With[{s = {1}~Join~Select[Range[4, 2*10^5], GCD @@ FactorInteger[#][[All, -1]] > 1 &]}, Select[Range@ Length@ s, PrimeQ[s[[#]] - #] &]] (* Michael De Vlieger, Aug 25 2021 *)

PARI

lista(nn) = {n = 0; for (pn=1, nn, if (pn==1 || ispower(pn), n++; if (isprime(pn - n), print1(n, ", "));););} \\ Michel Marcus, Jun 05 2013

Extensions

Edited by Georg Fischer, Aug 25 2021