Algorithmicx print first line number when numbering every n-th

Using the algorithmicx it is pretty easy to turn on or off line numbering or to number every n-th line. Taking this MWE (taken from the doc)

\documentclass{article}
\usepackage{algpseudocode}
\usepackage{algorithm}
\begin{document}
\begin{algorithm}[H]
\caption{Euclide's algorithm}\label{euclid}
\begin{algorithmic}[5]
\Procedure{Euclide}{$a,b$}\Comment{The g.c.d. of a and b}
\State $r\gets a\bmod b$
\While{$r\not=0$}\Comment{We have the answer if r is 0}
\State $a\gets b$
\State $b\gets r$
\State $r\gets a\bmod b$
\EndWhile\label{euclidendwhile}
\State \Return $b$\Comment{The gcd is b}
\EndProcedure
\end{algorithmic}
\end{algorithm}
\end{document}


In this example, the first numbered line is the 5-th. Is there a way to turn on the numbering on the first line ?

Subsequent question, is it possible to turn the numbering on any arbitrary line ?

You will have to update a specific macro to change the condition of printing:

\documentclass{article}
\usepackage{algpseudocode,algorithm}

\makeatletter
\def\ALG@step%
{%
\stepcounter{ALG@line}%
\stepcounter{ALG@rem}%
\ifnum\value{ALG@line}=1
% Print line number if it is 1
\alglinenumber{\arabic{ALG@line}}%
\else\ifnum\value{ALG@rem}=\ALG@numberfreq
% Print line number if the ALG@rem = \ALG@numberfreq
\setcounter{ALG@rem}{0}\alglinenumber{\arabic{ALG@line}}%
\fi\fi
}%
\makeatother

\begin{document}
\begin{algorithm}[H]
\caption{Euclide's algorithm}\label{euclid}
\begin{algorithmic}[5]
\Procedure{Euclide}{$a,b$}\Comment{The g.c.d.\ of~$a$ and~$b$}
\State $r \gets a \bmod b$
\While{$r \neq 0$}\Comment{We have the answer if~$r$ is~$0$}
\State $a \gets b$
\State $b \gets r$
\State $r \gets a \bmod b$
\EndWhile\label{euclidendwhile}
\State \Return $b$\Comment{The g.c.d.\ is~$b$}
\EndProcedure
\end{algorithmic}
\end{algorithm}
\end{document}


The adjustment to \ALG@step inserts a condition to check whether the line number is 1, and printing accordingly.

In general it would be possible to turn on the numbering on any arbitrary line, but the code is not set up for that.