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

1,1

Links

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

Wikipedia, Tetration

Formula

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

Example

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.

Prog

(PARI) slogint(n, b)=if(n<b, 0, slogint(logint(n, b), b)+1)
tetr(b, n)=my(t=b); for(i=2, n, t=b^t); t
list(lim)=my(v=List(), p, t); for(k=2, slogint(lim\=1, 2), p=1; while(tetr(1.0 * p=nextprime(p+1), k) <= 2*lim, listput(v, tetr(p, k)))); select(n->n<=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

Crossrefs

Cf. A000040.

Sequence in context: A046366 A227609 A219338 * A046361 A228167 A017569

Adjacent sequences: A275208 A275209 A275210 * A275212 A275213 A275214

Keyword

nonn

Author

Tyler Skywalker, Jul 19 2016

Extensions

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

Status

approved