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

3, 23, 25165823

Offset

0,1

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.

Links

Table of n, a(n) for n=0..2.

Robert Munafo, Versions of Ackermann's functions

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.

Example

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.

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 *)

Crossrefs

Cf. A083329.

Sequence in context: A224700 A352333 A355960 * A204578 A120085 A062834

Adjacent sequences: A264926 A264927 A264928 * A264930 A264931 A264932

Keyword

nonn

Author

Natan Arie Consigli, Nov 28 2015

Status

approved