Using rightmark to display section names on first page

Question

I am having problems getting the section name displayed on the top of my pages. I know \leftmark is the proper way to do this, but I would like that the section name is only displayed when no subsection name is present, and that it is not capitalized.

Explained in another way: This is a document of 3 pages. The first page has nothing in the header, I would like it to have "1 A section" in the header, but the following pages should remain the same:

\documentclass[twoside]{article}
\usepackage{fancyhdr}
%Header defined
\pagestyle{fancy}
\fancyhf{}
\fancyhead[RO]{\rightmark}
\fancyhead[LE]{\rightmark}
\begin{document}
\section{A section}
\newpage
\subsection{A subsection}
\newpage
\subsection{Another subsection}
\end{document}

Thanks in advance.

Answer 1

You must redefine \sectionmark to fill the right part of the mark. \rightmark always use the first mark, so if you have to sections or subsections on a page, you will get the first.

\documentclass[twoside]{article}
\usepackage{fancyhdr}
\renewcommand*\subsectionmark[1]{}
%Header defined
\pagestyle{fancy}
\fancyhf{}
\fancyhead[RO]{\rightmark}
\fancyhead[LE]{\rightmark}
\renewcommand*\sectionmark[1]{%
 \markboth{\thesection\hskip 1em\relax#1}{\thesection\hskip 1em\relax#1}}
\begin{document}
\section{A section}
\section{B section}
\newpage
\subsection{A subsection}
\subsection{B subsection}
\newpage
\subsection{Another subsection}
\end{document}