A014222 a(0) = 0; thereafter a(n+1) = 3^a(n).

0, 1, 3, 27, 7625597484987

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Alternative definition:

a(n+1) = H_4(3,n) the tetration (repeated exponentiation) of 3 times n.

For definition of and references concerning H_n(x,y) see A054871.

Next term is 12580...39387 and has 3638334640025 digits. - Shawn Ligocki (sligocki(AT)gmail.com), Oct 08 2009

Examples

			a(0) = H_4(3,-1)= 0;
a(1) = H_4(3,0) = 1;
a(2) = H_4(3,1) = 3;
a(3) = H_4(3,2) = 3^3 = 27;
a(4) = H_4(3,3) = 3^3^3 = 7625597484987;
a(5) = H_4(3,4) = 3^3^3^3 = 3^7625597484987 > 10^3638334640025.
		

Crossrefs

Cf. A014221 (a(n+1) = 2^a(n), or H_4(2,n)), A081651, A114561, A266199 (H_5(3,n)).

Programs

Mathematica

NestList[3^#&,0,4] (* Harvey P. Dale, Apr 04 2013 *)

Formula

a(n+1) = H_4(3,n) = 3^^n;

a(0) = 0, a(1) = 1, a(n+1) = 3^3^...^3 (n times).

Extensions

Revised using hyperoperation notation by Natan Arie Consigli, Jan 16 2016