PGFPlots marker at specific x values

How can I put a point (mark) in a PGFPlots graph at every x values?

For example, I have the following graph:

Produced by the following code:

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}

\begin{document}
\begin{tikzpicture}[baseline,trim axis left,trim axis right]
\begin{axis}[
y tick label style={
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=2,
/tikz/.cd
},
enlargelimits=true,
minor tick num=1,
width=\textwidth,
ylabel near ticks,
xlabel near ticks,
ytick={0,0.25,...,1},
xtick={0,1,...,4},
ylabel={Weight $w$},
xlabel={Slot $s$},
]
\end{axis}
\end{tikzpicture}
\end{document}


I tried using several mark primitives, mark step, mark phase, but was unable to produce the desired output. Desired output:

• You could e.g. add samples=5 to the second plot. – Stefan Pinnow Feb 12 '17 at 2:51

That could be done either by just adding samples=5 to your code or you can even do it a bit simpler.

For more details have a look at the comments in the code.

% used PGFPlots v1.14
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
% use this compat' level or higher to make use of the advanced positioning of labels
\pgfplotsset{compat=1.3}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
width=\textwidth,
ylabel={Weight $w$},
xlabel={Slot $s$},
% it is much simpler to use this key instead of defining the list
xtick distance=1,
minor tick num=1,
]
domain=0:4,
dashed,
] {0.31622776601683794^x};
% define the marker you want to use ...
mark=*,
% ... and how it shall look like
mark options={
color=orange,
},
% there is no need to use another domain here
% (so you can move it to the axis options and delete it
%  in the two \addplot' options
domain=0:4,
% it seems you only want the values at the integers, so
% define an appropriate number of samples
samples=5,
% and you want the marker on the left of the const plot'
const plot mark left,
thick,
% done all of the above there is no need for the floor function
] {0.31622776601683794^(x)};
\end{axis}
\end{tikzpicture}
\end{document}
`