A269769 Numbers of the form p^k - k where p is a prime number and k > 1.

2, 5, 7, 12, 23, 24, 27, 47, 58, 77, 119, 121, 122, 167, 238, 248, 287, 340, 359, 503, 527, 621, 723, 839, 959, 1014, 1328, 1367, 1679, 1847, 2037, 2180, 2194, 2207, 2397, 2807, 3120, 3479, 3719, 4084, 4487, 4910, 5039, 5327, 6239, 6553, 6856, 6887, 7919, 8179

Offset: 1

Author

Altug Alkan, Mar 04 2016

Keywords

• nonn

Comments

Primes of the form p^k - k where p is prime are 2, 5, 7, 23, 47, 167, 359, 503, ...

Subsequence of A057897.

A182474 is a subsequence.

Up to 10^14 all the terms have a unique representation as p^k - k. - Giovanni Resta, Mar 21 2017

Examples

			    2 is a term because   2 = 2^2 - 2.
    5 is a term because   5 = 2^3 - 3.
    7 is a term because   7 = 3^2 - 2.
   12 is a term because  12 = 2^4 - 4.
  121 is a term because 121 = 2^7 - 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A057897, A182474.

Programs

Maple

N:= 10000: # to get all terms <= N
P:= select(isprime, [$1..floor((N+2)^(1/2))]):
S:= {}:
for k from 2 do
  pmax:= floor((N+k)^(1/k));
  if pmax < 2 then break fi;
  S:= S union {seq(p^k-k, p = select(`<=`,P,pmax))};
od:
sort(convert(S,list)); # Robert Israel, Mar 21 2017