Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 BinaryIteratedLog

Source Notebook

Get the binary iterated logarithm of a positive number

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["BinaryIteratedLog"][z]

gives the binary iterated logarithm of z.

Details

The binary iterated logarithm is also known as inverse binary tetration. It is defined to be the smallest (integer) number of times that logarithm base 2 must be applied to a number to yield a result less than 1.

Examples

Basic Examples

BinaryIteratedLog is the inverse of binary tetration (repeated exponentiation):

In[1]:=
ResourceFunction["BinaryIteratedLog"][2^2^2^2]
Out[1]=

A slightly larger input shows a step-like jump in the value of BinaryIteratedLog:

In[2]:=
ResourceFunction["BinaryIteratedLog"][2^2^2^2 + 1]
Out[2]=

Make a table of the binary iterated logarithm of the first 30 integers:

In[3]:=
Table[ResourceFunction["BinaryIteratedLog"][i], {i, 0, 30}]
Out[3]=

Properties & Relations

BinaryIteratedLog gives zero for values less than 2:

In[4]:=
ResourceFunction["BinaryIteratedLog"] /@ {-10, -1, 0, 1}
Out[4]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 4.0.0 – 23 March 2023
  • 3.1.0 – 11 May 2021
  • 3.0.0 – 24 January 2020
  • 2.0.0 – 06 September 2019
  • 1.0.0 – 10 July 2019

Related Resources

License Information