A173566 a(n+1) = a(n)^a(n), with a(1) = 2.

2, 4, 256

Offset

1,1

Comments

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 Steinhaus-Moser 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)

Links

Michel Marcus, Table of n, a(n) for n = 1..4

Wikipedia, Steinhaus-Moser notation.

Example

a(3) = square(2) = triangle(triangle(2)) = triangle(2^2) = 4^4 = 256.
a(4) = 2^2048.
a(5) = 2^(2^2059).

Mathematica

RecurrenceTable[{a[1] == 2, a[n] == a[n - 1]^a[n - 1]}, a, {n, 4}] (* Vincenzo Librandi, Dec 17 2015 *)

Prog

(Magma) [n le 1 select 2 else Self(n-1)^Self(n-1): n in [1..4]]; // Vincenzo Librandi, Dec 17 2015

Crossrefs

Cf. A030798 ("preceding term"), A054874 (log base 2).

Sequence in context: A009673 A018770 A260755 * A271551 A058990 A343255

Adjacent sequences: A173563 A173564 A173565 * A173567 A173568 A173569

Keyword

nonn,bref

Author

Franklin T. Adams-Watters, Aug 03 2011

Status

approved