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%I #9 Jul 20 2016 10:46:49
%S 4,16,27,3125,65536,823543,285311670611,7625597484987,302875106592253,
%T 827240261886336764177,1978419655660313589123979,
%U 20880467999847912034355032910567
%N 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.
%H Charles R Greathouse IV, <a href="/A275211/b275211.txt">Table of n, a(n) for n = 1..79</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration">Tetration</a>
%F For any prime number, p, p tetrated x times, where x is any integer greater than 1, is a prime tetration.
%e a(1) = 2^^2 = 2^2 = 4.
%e a(2) = 2^^3 = 2^2^2 = 16.
%e a(3) = 3^^2 = 3^3 = 27.
%e a(4) = 5^^2 = 5^5 = 3125.
%o (PARI) slogint(n,b)=if(n<b,0,slogint(logint(n,b),b)+1)
%o tetr(b,n)=my(t=b); for(i=2,n, t=b^t); t
%o 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
%o (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
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Tyler Skywalker_, Jul 19 2016
%E a(5) inserted, a(10)-a(12) corrected by _Charles R Greathouse IV_, Jul 19 2016
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