This question is related to Biblatex-nature \textcite with superscript reference number, which shows how to make \textcite use superscript number.
But it does not work when I cite multiple references of the same author.
Here is a MWE (the result is something like Author1-3)
\documentclass{report}
\usepackage[citestyle=numeric-comp]{biblatex}
\usepackage{filecontents}
\begin{filecontents}{ABib.bib}
@article {a1,
AUTHOR = {Author},
TITLE = {A sample paper},
JOURNAL = {Sample journal},
VOLUME = {1},
YEAR = {2013},
NUMBER = {1},
PAGES = {1--2}}
@misc{a2,
AUTHOR = {Author},
TITLE = {A sample paper},
YEAR = {2013}}
@misc{a3,
AUTHOR = {Author},
TITLE = {A sample paper},
YEAR = {2013}}
\end{filecontents}
\addbibresource{ABib.bib}
%%%%%%%%
\makeatletter
\renewbibmacro*{textcite}{%
\iffieldequals{namehash}{\cbx@lasthash}
{\usebibmacro{cite:comp}}
{\usebibmacro{cite:dump}%
\ifbool{cbx:parens}
{\bibclosebracket\global\boolfalse{cbx:parens}}
{}%
\iffirstcitekey
{}
{\textcitedelim}%
\usebibmacro{cite:init}%
\ifnameundef{labelname}
{\printfield[citetitle]{labeltitle}}
{\printnames{labelname}}%
\addspace
\ifnumequal{\value{citecount}}{1}
{\usebibmacro{prenote}}
{}%
\mkbibsuperscript{\usebibmacro{cite:comp}}%
\stepcounter{textcitecount}%
\savefield{namehash}{\cbx@lasthash}}}
\makeatother
\begin{document}
\textcite{a1,a2,a3}
\end{document}
p.s. The original question was asked long time ago, and I am too new to have enough reputation to comment there, so I ask this new question here.