The next term, a(4), is 2^2048, with 617 digits.
From Natan Arie Consigli, Dec 01 2015: (Start)
Possible other sequence with the same first three entries:
a(1) = 2;
a(2) = Triangle(2);
a(3) = Square(2);
a(4) = Pentagon(2);
etc., where, in SteinhausMoser notation,
Triangle(n) = n^n;
Square(n) = Triangle(Triangle...(n)...) (with n inside n nested triangles);
Pentagon(n) = Square(Square...(n)...)(with n inside n nested squares);
etc.
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).
(End)
