A264929 a(n)= ackb(n,3) where ackb is the Ackermann-Burnell function.

3, 23, 25165823

Offset: 0

Author

Natan Arie Consigli, Nov 28 2015

Keywords

• nonn

Comments

ackb(x,z) =

{ x+2 for z=0

{

{ z for x=0, z>0

{

{ ackb(ackb(x-1,z), z-1) for x,z > 0

This version of the Ackermann function was created with the goal of creating the fastest growth with the least total number of operators, recursive calls, and conditional tests. Check the link for more details.

The reason we take ackb(n,3) is that it is the only sequence that can have its own entry in the OEIS.

a(3) has 7575669 decimal digits and is too big to be included in the data section.

Examples

			a(1) = ackb(1,3) = (3/2) ie3(sqrt(8), 1, 8/3) - 1 = (3/2)sqrt(8)^(8/3) - 1 = (3/2)2^((3/2)(8/3)) - 1 = (3/2)16 - 1 = 23.
		

Links

• Robert Munafo, Versions of Ackermann's functions

Crossrefs

Cf. A083329.

Programs

Mathematica

ie3[a_, b_, c_] := Nest[a^# &, c, b]; Table[(3/2) ie3[Sqrt@8, x, 8/3] - 1, {x, 0, 2}] (* Michael De Vlieger, Dec 01 2015 *)

Formula

a(n) = ackb(x,3) = (3/2) ie3(sqrt(8), x, 8/3) - 1 where ie3(a, b, c) = a^(a^( ... a^c))) (with b copies of a).

For proof, check the link above.