Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Binary
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 defind 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 (3)
BinaryIteratedLog is the inverse of binary tetration (repeated exponentiation):
| In[1]:= | ![ResourceFunction["BinaryIteratedLog"][2^2^2^2]](https://www.wolframcloud.com/obj/resourcesystem/images/837/837052f3-6c37-4eb8-bb12-0dbe930b4039/3-1-0/3f6244ebbc011024.png){kind=small} |
| 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]](https://www.wolframcloud.com/obj/resourcesystem/images/837/837052f3-6c37-4eb8-bb12-0dbe930b4039/3-1-0/19e23d7e34257841.png){kind=small} |
| Out[2]= |  |
Make a table of the binary iterated logarithm of the first 30 integers:
| In[3]:= | ![Table[ResourceFunction["BinaryIteratedLog"][i], {i, 0, 30}]](https://www.wolframcloud.com/obj/resourcesystem/images/837/837052f3-6c37-4eb8-bb12-0dbe930b4039/3-1-0/10643a7e3360addc.png){kind=small} |
| Out[3]= |  |
Publisher
Related Links
- Iterated Logarithm–Wolfram MathWorld
- Binary Logarithm–Wolfram MathWorld
- Logarithm–Wolfram MathWorld
- Natural Logarithm–Wolfram MathWorld
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
Related Symbols
License Information
This work is licensed under a Creative Commons Attribution 4.0 International License