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Function Repository Resource:

BinaryIteratedLog

Source Notebook

Implements the binary iterated logarithm function

Contributed by: Wolfram|Alpha math team

ResourceFunction["BinaryIteratedLog"][z]

gives the binary iterated logarithm of z.

Details and Options

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

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]=

Resource History

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