Drawing a circle with nodes shift with Tikz

I think something like this is what you're after.

\documentclass{beamer}
\usepackage{tikz}
% define a counter
\newcount\CircNum
% macro to hold a color name
\newcommand\Clr{black}
\begin{document}
\begin{frame}
% set up an animation, \CircNum changes from 1 to 17
% with each frame
\animatevalue<1-17>{\CircNum}{1}{17}
\begin{tikzpicture}
% draw the main circle
\node [circle, draw, minimum size=8cm] (c) {};

\foreach \a in {1,2,...,17}{
   % if \a is equal to \CircNum, set the color to blue
   % otherwise set it to black
   \ifnum\a=\the\CircNum
      \renewcommand\Clr{blue}
   \else
       \renewcommand\Clr{black}
   \fi
   % make a new node for the small circles
   \node[\Clr, % with the color defined by the macro
         draw, thick, % draw the outline
         fill, % fill it
         minimum size=5mm, % set the size
         circle, % circular shape
         label={[\Clr]\a*360/17+180:\a} % add the number on the inside
         ] at (c.\a*360/17) % position it on the edge of the main circle
          {};
}
\end{tikzpicture}
\end{frame}
\end{document}

Here are the first three slides of the PDF:

Welcome to TeX.SE!

Here is a solution that borrows \int_step_variable:nnnNn from expl3:

\documentclass{beamer}
\usepackage{expl3}
\usepackage{tikz}

\ExplSyntaxOn
% Borrow a loop macro from expl3
\cs_set_eq:NN \intstepvariable \int_step_variable:nnnNn
\ExplSyntaxOff

\begin{document}

\begin{frame}{Circles in circle}
\begin{center}
\begin{tikzpicture}
  \def\nsteps{10}
  \def\bigcircleradius{3cm}
  \def\smallcirclewidth{0.5cm}

  % The big circle
  \node[circle, minimum width=2*\bigcircleradius, draw] (C) {};

  % The small circles and their labels
  \intstepvariable{0}{1}{\nsteps - 1}{\i}{% {init}{step}{final}{variable}
    \pgfmathsetmacro{\angle}{90 - \i*360/\nsteps}
    \pgfmathsetmacro{\otherside}{\angle+180}
    \pgfmathsetmacro{\iplusone}{int(\i+1)}
    \pgfmathsetmacro{\iplustwo}{int(\i+2)}

    \uncover<\iplustwo-> {
      \node[circle, draw, minimum width=2*\smallcirclewidth,
            label=\otherside:\iplusone] at (C.\angle) {};
    }
    \uncover<\iplustwo> {   % fill one small circle per frame
      \node[circle, fill=red!20, minimum width=2*\smallcirclewidth]
        at (C.\angle) {};
    }
  }

\end{tikzpicture}
\end{center}
\end{frame}

\end{document}

...

...

Note: as an alternative to the following code:

\pgfmathsetmacro{\iplustwo}{int(\i+2)}

(...)

\uncover<\iplustwo-> { (...) }
\uncover<\iplustwo>  { (...) }

one could use, assuming e-TeX extensions are available:

\uncover<\the\numexpr \i+2\relax-> { (...) }
\uncover<\the\numexpr \i+2\relax>  { (...) }

Now, let's redo the same beamer presentation, but using a more straightforward order (small circles at angles 1*360/10, 2*360/10, ..., 10*360/10 degrees, respectively). The main code is written in a (slightly) different way from the previous example: it uses two loops and the \pause macro from beamer, whereas the first example did everything in one loop, and used only \uncover.

\documentclass{beamer}
\usepackage{expl3}
\usepackage{tikz}

\ExplSyntaxOn
% Borrow a loop macro from expl3
\cs_set_eq:NN \intstepvariable \int_step_variable:nnnNn
\ExplSyntaxOff

\begin{document}

\begin{frame}{Circles in circle}
\begin{center}
\begin{tikzpicture}
  \def\nsteps{10}
  \def\bigcircleradius{3cm}
  \def\smallcirclewidth{0.5cm}

  % The big circle
  \node[circle, minimum width=2*\bigcircleradius, draw] (C) {};

  % The filled circles: highlight a single small circle on each frame starting
  % from frame 2.
  \intstepvariable{2}{1}{\nsteps+1}{\i}{% {init}{step}{final}{variable}
    \pgfmathsetmacro{\angle}{(\i-1)*360/\nsteps}
    \uncover<\i>{
      \node[circle, fill=red!20, minimum width=2*\smallcirclewidth]
        at (C.\angle) {};
    }
  }

  % The unfilled circles and their labels
  \intstepvariable{1}{1}{\nsteps}{\i}{% {init}{step}{final}{variable}
    \pgfmathsetmacro{\angle}{\i*360/\nsteps}
    \pgfmathsetmacro{\otherside}{\angle+180}

    \pause
    \node[circle, draw, minimum width=2*\smallcirclewidth, label=\otherside:\i]
      at (C.\angle) {};
  }

\end{tikzpicture}
\end{center}
\end{frame}

\end{document}

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