Example with clubsuit (no ntheorem)

Question

I would like an example environment which is numbered according to theorems (e.g. theorem 1, example 2, theorem 3, example 4, ...) and ends with a clubsuit. I've already seen this solution, but I would rather have one which doesn't use the ntheorem package; either by creating a new environment, or by rewriting the existing one (e.g. the proof environment). I'm not particularly experienced with LaTex, so I'm asking this.

This is the code I have so I can get started. I can live with the error for now.

\documentclass{amsart}

% \usepackage[utf8]{inputenc}
\usepackage{amsthm}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{example}[theorem]{Example}
\newenvironment{example}{\paragraph{Example:}}{\hfill$\clubsuit$\vspace{10pt}}
% produces Error: Command \example already defined.

It mostly works. It is numbered according to theorem, and ends with a clubsuit:

\begin{example}
    First example.
\end{example}

However, there are some issues, as illustrated below:

\begin{example}
    Second example.
\end{example}
Line after second example breaks it.

This can be fixed by adding a new line as follows:

\begin{example}
    Third example.
\end{example}

A line after a newline after the third example is okay.

But I'd rather not have to do this fix in the first place. Also, the environment doesn't work with equations.

\begin{example}
    Example ending on an equation (qedhere does not work)
    \begin{equation*}
        a = b.
    \end{equation*}
\end{example}

Unlike the proof environment, \qedhere does not work. Similar issue goes with itemize/enumerate. In summary, I would like a minimal, non-ntheorem-based example environment, which is essentially a copy of the proof environment, but the QED symbol is replaced by a clubsuit (such that the \qedhere command or equivalent can bring the clubsuit into an ending equation). I'm sure there is a simpler solution than what I have.

---

Update. The following solution adapted from here is very close to what I want:

\newcommand{\newmarkedtheorem}[1]{%
  \newenvironment{#1}
    {\pushQED{\hfill$\clubsuit$}\csname inner@#1\endcsname}
    {\popQED\csname endinner@#1\endcsname}%
  \newtheorem{inner@#1}%
}
\newmarkedtheorem{example}[theorem]{Example}

However, there is still an issue with the equation and align environments.

\begin{example}
    Example ending in align environment:
    \begin{align*}
        1 + 1 + 1 &= 1 + 2\\
        &= 3.\qedhere
    \end{align*}
\end{example}

Answer 1

The problem is with \pushQED{\hfill$\clubsuit$}. You really need \pushQED{\qed} or to define something else along the line of \qed.

The easiest way is to add an optional argument for the symbol to use.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}

\newcommand{\newmarkedtheorem}[2][\openbox]{%
  \newenvironment{#2}
    {\renewcommand{\qedsymbol}{#1}\pushQED{\qed}\csname inner@#2\endcsname}
    {\popQED\csname endinner@#2\endcsname}%
  \newtheorem{inner@#2}%
}

\newtheorem{theorem}{Theorem}
\newmarkedtheorem[$\clubsuit$]{example}[theorem]{Example}
\newmarkedtheorem[$\diamondsuit$]{exercise}{Exercise}

\begin{document}

\begin{example}
An example.
\end{example}

\begin{exercise}
An exercise.
\end{exercise}

\begin{example}
    Example ending in align environment:
    \begin{align*}
        1 + 1 + 1 &= 1 + 2\\
        &= 3.\qedhere
    \end{align*}
\end{example}

\end{document}

Using no optional argument would default to the standard \openbox.