%I #45 Jul 08 2024 11:12:34
%S 2,4,256
%N a(n+1) = a(n)^a(n), with a(1) = 2.
%C The next term, a(4), is 2^2048, with 617 digits.
%C From _Natan Arie Consigli_, Dec 01 2015: (Start)
%C Possible other sequence with the same first three entries:
%C a(1) = 2;
%C a(2) = Triangle(2);
%C a(3) = Square(2);
%C a(4) = Pentagon(2);
%C etc., where, in Steinhaus-Moser notation,
%C Triangle(n) = n^n;
%C Square(n) = Triangle(Triangle...(n)...) (with n inside n nested triangles);
%C Pentagon(n) = Square(Square...(n)...)(with n inside n nested squares);
%C etc.
%C Start with a(1) = 2, a(2) = triangle(2) = 4, a(3) = square(2) = 256, a(4) = pentagon(4) = 256^^256 (power tower of 256s with height 256).
%C (End)
%H Michel Marcus, <a href="/A173566/b173566.txt">Table of n, a(n) for n = 1..4</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Steinhaus-Moser_notation">Steinhaus-Moser notation</a>.
%e a(3) = square(2) = triangle(triangle(2)) = triangle(2^2) = 4^4 = 256.
%e a(4) = 2^2048.
%e a(5) = 2^(2^2059).
%t RecurrenceTable[{a[1] == 2, a[n] == a[n - 1]^a[n - 1]}, a, {n, 4}] (* _Vincenzo Librandi_, Dec 17 2015 *)
%o (Magma) [n le 1 select 2 else Self(n-1)^Self(n-1): n in [1..4]]; // _Vincenzo Librandi_, Dec 17 2015
%Y Cf. A030798 ("preceding term"), A054874 (log base 2).
%K nonn,bref
%O 1,1
%A _Franklin T. Adams-Watters_, Aug 03 2011