In total, I don't recommend this pagenumbering at all, since it will lead to recto pages with even page numbers.
The output of \thepage must be changed -- either use a \renewcommand{\thepage}{....} or a more clever way, see the example at the bottom of this answer with \pagenumbering{weird} ;-)
Here's a version that changes the 4th page number to be \pi and continues with 4 then.
Please note that \pagenumbering etc does change the numbering again and hyperref could be confused by this!
\documentclass{memoir}
\usepackage{everypage}
\usepackage{blindtext}
\newif\ifpipage
\let\thepageorig\thepage
\AddEverypageHook{%
\ifnum\value{page} = 4
\renewcommand{\thepage}{$\pi$}%
\global\pipagetrue
\else
\ifpipage
\addtocounter{page}{-1}
\global\pipagefalse
\fi
\let\thepage\thepageorig
\fi
}
\begin{document}
\blindtext[50]
\end{document}
Better version
\documentclass{memoir}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{blindtext}
\makeatletter
\newcommand{\@weird}[1]{%
\ifnum#1< 4
\@arabic{#1}%
\else
\ifnum#1=4
\texorpdfstring{\large$\pi$}{π}%
\else
\@arabic{\numexpr#1-1}%
\fi
\fi
}
\makeatother
\usepackage{hyperref}
\begin{document}
\frontmatter
\tableofcontents
\mainmatter
\clearpage
\pagenumbering{weird}
\chapter{First}
\blindtext[50]
\chapter{Second}
\blindtext[50]
\end{document}

Other version -- now with \sqrt{2}, e and \pi ;-)
\pagenumbering{nerdy} does it all ;-)
\documentclass{memoir}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{siunitx}
\usepackage{blindtext}
\usepackage{hyperref}
\newif\ifusesymbols
\usesymbolstrue
\makeatletter
\ifusesymbols
\newcommand{\sqrttwocontent}{\texorpdfstring{$\sqrt{2}$}{2\textsuperscript{0,5}}}
\newcommand{\eulercontent}{\texorpdfstring{$e$}{e}}
\newcommand{\picontent}{\texorpdfstring{$\pi$}{π}}
\else
\newcommand{\sqrttwocontent}{\num{1.41421}}
\newcommand{\eulercontent}{\num{2.71828}}%
\newcommand{\picontent}{\num{3.14159}}%
\fi
\newcommand{\@weird}[1]{%
\ifnum#1< 4
\@arabic{#1}%
\else
\ifnum#1=4
\picontent
%\texorpdfstring{\large$\pi$}{π}
\else
\@arabic{\numexpr#1-1}
\fi
\fi
}
\newcommand{\@nerdy}[1]{%
\boldmath
\ifnum#1< 2
\@arabic{#1}%
\else
\ifcase#1
\or\or
\sqrttwocontent
\or
\eulercontent%
\or \picontent%
\else
\@arabic{\numexpr#1-1}%
\fi
\fi
\unboldmath
}
\makeatother
\begin{document}
\frontmatter
\tableofcontents
\mainmatter
\clearpage
\pagenumbering{nerdy}
\chapter{First}
\blindtext[3]
\section{Foo}
\blindtext[4]
\chapter{Second}
\blindtext[3]
\section{Foobar}
\blindtext[3]
\end{document}

e=2.718281828is missing then too ;-) – Apr 23 '16 at 10:08pi? – Apr 23 '16 at 10:11\pior page 4. I just want to shift the numbering one page in order to include pi. (Just for fun, not a necessity.) – Thomas Apr 23 '16 at 10:15