Numero sign with double underline and matching font

Similar approach with a TABstack. It adapts to fontsize changes.

\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{yfonts}
\usepackage{tabstackengine}
\newcommand\Number{\begingroup\setstackgap{S}{0.08ex}%
  \ensureTABstackMath{\stackinset{r}{-.05em}{c}{}{\tabbedShortunderstack{%
  \scalebox{.7}{$\scriptscriptstyle o$}\\\TABrule\\\TABrule}}{$\mathcal{N}$}}%
  \endgroup}
\begin{document}
\frakfamily

\Number\,4

\Huge\Number\,4
\end{document}

This yields a similar result as in the example, and it adapts well to different font sizes.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pict2e}
\newlength{\fslength}
\newlength{\fthickness}
\DeclareFontFamily{U}{eus}{\skewchar\font'60}
\DeclareFontShape{U}{eus}{m}{n}{%
    <5><6><7><8><9>gen*eusm%
    <10><10.95><12><14.4><17.28><20.74><24.88>eusm10}{}
\DeclareMathAlphabet\EuScript{U}{eus}{m}{n}
\makeatletter
\newcommand{\Number}[1]{%
    \setlength{\fslength}{\f@size pt}%
    \setlength{\fthickness}{.04\fslength}%
    \pdfsave\pdfliteral{1 0 .25 1 0 0 cm}\rlap{$\EuScript{N}$}\pdfrestore%
    \phantom{$\EuScript{N}$}%
    \rule[.16\fslength]{.25\fslength}{\fthickness}\hspace*{-.23\fslength}%
    \rule[.24\fslength]{.25\fslength}{\fthickness}\hspace*{-.30\fslength}%
    \raisebox{.24\fslength}[.4\fslength]{%
        \centering%
        \setlength{\unitlength}{\fslength}%
        \begin{picture}(.3,.3)
            \linethickness{\fthickness}
            \put(.2,.2){\circle{.2}}
        \end{picture}%
    } #1%
}
\makeatother

\begin{document}
{\scriptsize This is \Number{4} for a test.}

{\small This is \Number{4} for a test.}

This is \Number{4} for a test.

{\large This is \Number{4} for a test.}

{\Large This is \Number{4} for a test.}
\end{document}

As it is, this example has to be compiled with pdfLaTeX. If it were to be compiled with XeLaTeX or LuaLaTeX, the lines

\pdfsave\pdfliteral{1 0 .25 1 0 0 cm}\rlap{$\EuScript{N}$}\pdfrestore%
\phantom{$\EuScript{N}$}%

would have to be changed. The N symbol that I used in this example is a slanted version of the N in Euler script font, but I'm not sure how it can be slanted using other compilers. In any case, the above lines could be changed to simply

$\mathcal{N}$\hspace*{-.2\fslength}%

to yield a similar result than in the picture given at the beginning, but with a computer modern \mathcal{N}.

Not as wide as in the example, but quite similar. A Cyrillic “number sign” with a second bar added.

\documentclass{article}
\usepackage{pict2e,picture}
\usepackage[T2A,T1]{fontenc}

\newcommand{\simplens}{%
  {\normalfont\fontencoding{T2A}\itshape\symbol{'235}}%
}
\DeclareRobustCommand{\ns}{%
  \simplens
  \begin{picture}(0,0)
  \linethickness{0.065ex}
  \roundcap
  \put(-0.225em,0.3ex){\line(1,0){0.215em}}
  \end{picture}%
}

\begin{document}

Some text and \ns~1.

{\Large \ns~4}

\end{document}