\relax 
\ifx\hyper@anchor\@undefined
\global \let \oldcontentsline\contentsline
\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global \let \oldnewlabel\newlabel
\gdef \newlabel#1#2{\newlabelxx{#1}#2}
\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\let \contentsline\oldcontentsline
\let \newlabel\oldnewlabel}
\else
\global \let \hyper@last\relax 
\fi

\citation{OEIS}
\citation{OEIS}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\@writefile{toc}{\contentsline {section}{\numberline {2} The main theorems }{3}{section.2}}
\newlabel{sec2}{{2}{3}{\relax }{section.2}{}}
\newlabel{ThS}{{2.1}{3}{\relax }{theorem.2.1}{}}
\newlabel{EqSF0}{{1}{3}{\relax }{equation.1}{}}
\newlabel{EqSFR}{{2}{3}{\relax }{equation.2}{}}
\newlabel{EqSF1}{{3}{3}{\relax }{equation.3}{}}
\@writefile{toc}{\contentsline {paragraph}{Proof.}{3}{table.1}}
\newlabel{EqBIN1}{{4}{3}{\relax }{equation.4}{}}
\newlabel{EqBIN2}{{5}{3}{\relax }{equation.5}{}}
\newlabel{EqBIN3}{{6}{4}{\relax }{equation.6}{}}
\newlabel{EqSeqD}{{7}{5}{\relax }{equation.7}{}}
\newlabel{ThD}{{2.2}{5}{\relax }{theorem.2.2}{}}
\newlabel{EqDF0}{{8}{5}{\relax }{equation.8}{}}
\newlabel{EqDFR}{{9}{6}{\relax }{equation.9}{}}
\newlabel{EqDF1}{{10}{6}{\relax }{equation.10}{}}
\@writefile{toc}{\contentsline {paragraph}{Proof.}{6}{equation.10}}
\newlabel{ThT}{{2.3}{6}{\relax }{theorem.2.3}{}}
\newlabel{EqTF0}{{11}{6}{\relax }{equation.11}{}}
\newlabel{EqTFR}{{12}{6}{\relax }{equation.12}{}}
\newlabel{EqTF1}{{13}{6}{\relax }{equation.13}{}}
\newlabel{EqTD1}{{14}{6}{\relax }{equation.14}{}}
\newlabel{EqC}{{15}{6}{\relax }{equation.15}{}}
\@writefile{toc}{\contentsline {paragraph}{Proof.}{6}{equation.15}}
\newlabel{EqCross3}{{16}{6}{\relax }{equation.16}{}}
\newlabel{EqD}{{17}{7}{\relax }{equation.17}{}}
\newlabel{EqE}{{18}{7}{\relax }{equation.18}{}}
\newlabel{EqE2}{{19}{7}{\relax }{equation.19}{}}
\newlabel{EqCross1}{{20}{7}{\relax }{equation.20}{}}
\newlabel{EqCross2}{{21}{8}{\relax }{equation.21}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Further properties}{8}{section.3}}
\newlabel{sec3}{{3}{8}{\relax }{section.3}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Trajectories}{8}{subsection.3.1}}
\newlabel{sec3.1}{{3.1}{8}{\relax }{subsection.3.1}{}}
\newlabel{Th2}{{3.1}{8}{\relax }{theorem.3.1}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}Fixed points}{9}{subsection.3.2}}
\newlabel{sec3.2}{{3.2}{9}{\relax }{subsection.3.2}{}}
\newlabel{EqFA}{{22}{9}{\relax }{equation.22}{}}
\newlabel{EqFB}{{23}{9}{\relax }{equation.23}{}}
\newlabel{EqFC}{{24}{9}{\relax }{equation.24}{}}
\newlabel{EqFD}{{25}{9}{\relax }{equation.25}{}}
\newlabel{ThF}{{3.2}{9}{\relax }{theorem.3.2}{}}
\newlabel{EqFIX1}{{26}{9}{\relax }{equation.26}{}}
\citation{OEIS}
\citation{ONAG}
\citation{CS86}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}The number of terms in the formulae for $t(n)$ and $s(n)$}{10}{subsection.3.3}}
\newlabel{EqTA}{{27}{10}{\relax }{equation.27}{}}
\newlabel{ThTA}{{3.3}{10}{\relax }{theorem.3.3}{}}
\newlabel{EqTB}{{28}{10}{\relax }{equation.28}{}}
\newlabel{EqTC}{{29}{10}{\relax }{equation.29}{}}
\citation{HW}
\citation{HW}
\newlabel{ThTA2}{{3.4}{11}{\relax }{theorem.3.4}{}}
\newlabel{EqTD2}{{30}{11}{\relax }{equation.30}{}}
\newlabel{EqTD2a}{{31}{11}{\relax }{equation.31}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}Average order}{11}{subsection.3.4}}
\newlabel{Th3}{{3.5}{11}{\relax }{theorem.3.5}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Related sequences}{11}{section.4}}
\newlabel{sec4}{{4}{11}{\relax }{section.4}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Two permutations of the nonnegative integers}{11}{subsection.4.1}}
\newlabel{secPerm}{{4.1}{11}{\relax }{subsection.4.1}{}}
\bibcite{ONAG}{1}
\bibcite{CS86}{2}
\bibcite{HW}{3}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}A second downward-sloping version}{12}{subsection.4.2}}
\newlabel{sec4.1}{{4.2}{12}{\relax }{subsection.4.2}{}}
\bibcite{OEIS}{4}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces The sloping binary numbers $s(n)$ are obtained by reading the array of binary numbers along upward-sloping diagonals. The table gives $s(0), \ldots  , s(32)$ in both base 2 and base 10, as well as the values of $(s(n)-n)/2$.}}{14}{table.1}}
\newlabel{T1}{{1}{14}{\relax }{table.1}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces By using 2's-complement notation for the binary expansion of negative numbers, $s(n)$ can be defined for all $n \in {\@mathbb Z}$. The values $\{s(n): n \le -1 \}$ are the numbers missing from $\{s(n) : n \ge 0\}$.}}{15}{table.2}}
\newlabel{T2}{{2}{15}{\relax }{table.2}{}}
