% Imposition of apology-book.pdf in signatures: two A5 pages on each side of
% a landscape A4 sheet, in the right order to fold in half and sew.
% Each signature has at most \sheets sheets (4 pages per sheet); the
% sheets are shared out evenly among the signatures.
% Print on both sides, flipping on the short edge; fold each signature,
% stack the signatures in order and sew them.
% Compile apology-book.tex first.
\documentclass{article}
\usepackage[a4paper,landscape]{geometry}
\usepackage{pdfpages}
\usepackage{iftex}
\def\bookpdf{apology-book.pdf}
\def\sheets{6}% sheets per signature, at most (a single signature: 999)
\newcount\Npages \newcount\Nsheets \newcount\Nsigs \newcount\Sbase \newcount\Sextra
\newcount\sig \newcount\nsheets \newcount\npages \newcount\before \newcount\j
\ifPDFTeX \pdfximage{\bookpdf}\Npages=\pdflastximagepages
\else\ifXeTeX \Npages=\XeTeXpdfpagecount"\bookpdf"\relax
\else \saveimageresource{\bookpdf}\Npages=\lastsavedimageresourcepages
\fi\fi
\Nsheets=\Npages \advance\Nsheets 3 \divide\Nsheets 4              % sheets in all
\Nsigs=\Nsheets \advance\Nsigs\sheets \advance\Nsigs -1 \divide\Nsigs\sheets
\Sbase=\Nsheets \divide\Sbase\Nsigs                         % sheets per signature
\Sextra=\Sbase \multiply\Sextra\Nsigs \advance\Sextra -\Nsheets
\multiply\Sextra -1                                     % signatures with one sheet more
% order within each signature of p pages (a = pages of the earlier signatures):
% a+p,a+1 | a+2,a+p-1 | a+p-2,a+3 | ...  (page > total = blank)
\def\pg#1{\ifnum#1>\Npages {}\else #1\fi}
\def\order{}
\def\signature{%
  \nsheets=\Sbase \ifnum\sig<\Sextra \advance\nsheets 1 \fi
  \npages=\nsheets \multiply\npages 4
  \j=0
  \loop\ifnum\j<\nsheets
    \edef\order{\order
      \pg{\the\numexpr\before+\npages-2*\j\relax},\pg{\the\numexpr\before+2*\j+1\relax},%
      \pg{\the\numexpr\before+2*\j+2\relax},\pg{\the\numexpr\before+\npages-2*\j-1\relax},}%
    \advance\j 1
  \repeat
  \advance\before\npages \advance\sig 1 }
\def\signatures{\ifnum\sig<\Nsigs \signature\expandafter\signatures\fi}
\signatures
\def\dropcomma#1,\dropend{#1}\edef\order{\expandafter\dropcomma\order\dropend}% the final comma
\begin{document}
\edef\x{\noexpand\includepdf[pages={\order},nup=2x1]{\bookpdf}}\x
\end{document}