A275211 Numbers of the form p^^k, where p is prime, k > 1, and ^^ is the tetration operator: x^^y = x^x^...^x with y copies of x.

4, 16, 27, 3125, 65536, 823543, 285311670611, 7625597484987, 302875106592253, 827240261886336764177, 1978419655660313589123979, 20880467999847912034355032910567

Offset: 1

Author

Tyler Skywalker, Jul 19 2016

Keywords

• nonn

Examples

			a(1) = 2^^2 = 2^2 = 4.
a(2) = 2^^3 = 2^2^2 = 16.
a(3) = 3^^2 = 3^3 = 27.
a(4) = 5^^2 = 5^5 = 3125.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..79
• Wikipedia, Tetration

Crossrefs

Cf. A000040.

Programs

PARI

slogint(n,b)=if(nn<=lim, Set(v)) \\ Charles R Greathouse IV, Jul 19 2016

PARI

is(n)=my(p,e); e=isprimepower(n,&p); e && (e==p || (e%p==0 && is(e))) \\ Charles R Greathouse IV, Jul 19 2016

Formula

For any prime number, p, p tetrated x times, where x is any integer greater than 1, is a prime tetration.

Extensions

a(5) inserted, a(10)-a(12) corrected by Charles R Greathouse IV, Jul 19 2016