Enumeration in powers of 2

Question

I would like to enumerate a list, but instead of the standard numbering

 1. bar
 2. bar
 3. bar
 4. bar
 5. bar

I would like the labels to be powers of 2 (automatically generated):

 1. bar
 2. bar
 4. bar
 8. bar
16. bar

etc. Can this be done with enumitem or pgf?

Answer 1

Examples with xfp or pgfmath are shown below. Note that the enumi counter is for the outermost level, if this is a nested list you need enumii/enumiii/enumiv, depending on the level of nesting.

\documentclass{article}
\usepackage{enumitem}
\usepackage{xfp}
\usepackage{pgfmath}
\begin{document}
\begin{enumerate}[label={\protect\fpeval{2^(\value{enumi}-1)}.}]
\item
foo
\item
bar
\item
baz
\item
foo
\item
bar
\item
baz
\item
foo
\item
bar
\item
baz
\end{enumerate}
\begin{enumerate}[label={\protect\pgfmathparse{int(2^(\value{enumi}-1))}\protect\pgfmathresult.}]
\item
foo
\item
bar
\item
baz
\item
foo
\item
bar
\item
baz
\item
foo
\item
bar
\item
baz
\end{enumerate}
\end{document}

Answer 2

No other package used, only enumitem's way of adding enumerate counter and evaluating with \numexpr, defining a new list in order to keep the regular enumerate list clean.

\documentclass{article}
\usepackage{enumitem}

\newcounter{powercntr}
\makeatletter
\DeclareRobustCommand{\poweroftwocalc}[1]{%
  \ifnum1<\value{#1}%
  \setcounter{powercntr}{\numexpr\c@powercntr*2}
  \fi
}
\def\poweroftwo#1{\poweroftwocalc{#1}\expandafter\@poweroftwo\csname the#1\endcsname}
\def\@poweroftwo#1{\thepowercntr}

\AddEnumerateCounter{\poweroftwo}{\@poweroftwo}{4096}

\newlist{powerlist}{enumerate}{1}
\setlist[powerlist,1]{before=\setcounter{powercntr}{1}}

\makeatother



\begin{document}
\begin{powerlist}[label={\poweroftwo*}]
\item And
\item Now
\item For
\item Something
\item Completely 
\item Different
\item Was
\item Said
\item Very
\item Frequently
\item In
\item Monty
\item Python's
\item Flying
\item Circus
\end{powerlist}
\end{document}

Answer 3

No other packages used, no e-TeX needed. Basically a rip-off of @ChristianHupfer's idea.

\documentclass{article}
\usepackage{enumitem}

\newcounter{powercntr}

\DeclareRobustCommand{\updatepowercntr}[1]%
  {\arabic{powercntr}\addtocounter{powercntr}{\value{powercntr}}}

\newlist{powerlist}{enumerate}{1}
\setlist[powerlist,1]{before=\setcounter{powercntr}{1}}

\begin{document}
\begin{powerlist}[label={\updatepowercntr*}]
\item And
\item Now
\item For
\item Something
\item Completely 
\item Different
\item Was
\item Said
\item Very
\item Frequently
\item In
\item Monty
\item Python's
\item Flying
\item Circus
\end{powerlist}
\end{document}

Answer 4

Here is a version demonstrating \AddEnumerateCounter and using xintcore for the arithmetic. This way you can start at any (positive) power of 2 you choose and nesting is no problem.

\documentclass{article}

\usepackage{enumitem,xintcore}

\AddEnumerateCounter*{\poweroftwo}{\internalpoweroftwoname}{1}
\newcommand{\poweroftwo}[1]{\xintiiPow{2}{\value{#1}}}

\begin{document}

\begin{enumerate}[label={\poweroftwo*},start={19}]
\item A
\item list
\item enumerated
\item with
\item powers
\item of
\item two
\item starting
\item at
\item the
\item initial
\item value
\item 5
\item 2
\item 4
\item 2
\item 8
\item 8
\end{enumerate}

\end{document}

You probably want to use this with leftmargin=*,widest*=38.

I originally used the bigintcalc package but @jfbu kindly pointed out that xintcore is significantly faster. For bigintcalc the syntax

\newcommand{\poweroftwo}[1]{\bigintcalcPow{2}{\number\value{#1}}}

with \number is needed.

Note I have simplified the syntax from the enumitem manual. We no longer need a helper macro, and can avoid @ in names, so do not have to encase in \makeatletter...\makeatother. The second argument of \AddEnumerateCounter looks like a macro, but is actually stripped of the leading \ to produce a character string to build internal names in enumitem.