Special arrow: both dotted and normal

Question

I would like to make use of a special arrow that I cannot find anywhere in the literature: namely half dotted and half normal, so like $\cdots\rightarrow$, but then normal sized. Does anyone know if such a command exist and if not how one can make it?

Answer 1

A poor man's solution:

\documentclass{article}
\usepackage{amssymb}% for \dashrightarrow
\newcommand*{\halfdotsrightarrow}{%
  \mathrel{%
    {\cdotp}{\cdotp}{\cdotp}{\rightarrow}%
  }%
}
\begin{document}
  $\dashrightarrow$
  $\halfdotsrightarrow$
\end{document}

Answer 2

A rich man's (I mean, overkill) solution:

\documentclass{article}
\usepackage{tikz}
\def\tikzhalfdotsrightarrow{\tikz[baseline=-.5ex, line cap=round]
   \draw (0,0) [densely dotted] -- (1ex,0) edge[solid, -to] (2.2ex,0);%
}    
\newcommand*{\halfdotsrightarrow}{\mathrel{\tikzhalfdotsrightarrow}}

\begin{document}
% I put a normal arrow and the new arrow in a expression to compare their sizes    
\[
  \frac{|a|\to|b|}{|a|\halfdotsrightarrow|b|}
\]
\end{document}

It can be seen that the length of the tail is the same (I forced it), but the width of the tip is smaller in the tikz version. I don't know how to enlarge it.

UPDATE: The following definition causes the "dotted" part to appear really dotted, and not dashed.

\def\tikzhalfdotsrightarrow{\tikz[baseline=-.5ex, line cap=round]
   \draw (0,0) [dash pattern=on .01pt off 1.4pt] -- (1ex,0) edge[solid, -to] (2.2ex,0);%
}