Tukukkk

I am trying to produce a spiral of numbers from 1 through 101 with the following properties:

-- multiples of 5 are in a node shaped like pentagon

-- there is a special starburst node at numbers 3, 6, 11, 13, 17, 23, 29, 37, 43, 52, 56, 61, 63, 68, 69, 71, 72, 80, 91, 99.

(I think one could use the shapes.geometric library to achieve both of these if only I could figure out how to switch styles at specific values of x in the loop below.)

Here is where I am (with help from here):

documentclass[parskip]{scrartcl}

usepackage[margin=15mm]{geometry}

usepackage{stix}

usepackage{tikz}

usetikzlibrary{shapes.geometric}

usetikzlibrary{calc}

usepackage{pifont}

usepackage{wasysym}

usepackage{graphicx}



begin{document}

hspace{0pt} vfill

begin{center}

  newcounter{cntRoot}

  begin{tikzpicture}

    coordinate (a) at (0,0);

    coordinate (b) at (0:1);

    foreach x in {1,...,100}{%

            coordinate (c) at ($(b)!0.9cm!270:(a)$);

            setcounter{cntRoot}{x}

            addtocounter{cntRoot}{1}

            node[fill=white,draw,circle,inner sep=1pt] at (c)

                {$thecntRoot$};

            coordinate (b) at (c);

          };

        end{tikzpicture}

      end{center}

vfill

end{document}

I tried to implement ideas from this answer without much success. Any help would be much appreciated!

I am sure that there is a more efficient way of dealing with your starbursts (for example, using LaTeX3), but the code below deals with them by first defining a comma separated list of special numbers and them looping through all of them to see if there is a match. The numbers mod 5 are easy to deal with using pgfmathparseresult.

The end result is then:

Here is the code:

documentclass[parskip]{scrartcl}

usepackage[margin=15mm]{geometry}

usepackage{stix}

usepackage{tikz}

usetikzlibrary{shapes,shapes.geometric,calc}

usepackage{pifont}

usepackage{wasysym}

usepackage{graphicx}

newififnotfound% to mark the stars as we print them

newcommandstarbursts{3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99}

begin{document}



  begin{tikzpicture}

    coordinate (a) at (0,0);

    coordinate (b) at (0:1);

    foreach x in {1,...,100}{%

        coordinate (c) at ($(b)!0.9cm!270:(a)$);

        pgfmathparse{int(mod(x,5))}

        ifnumpgfmathresult=0

        node[fill=white,draw,regular polygon, regular polygon sides=5,inner sep=1pt] at (c) {$x$};

        else

          notfoundtrue% this will mark any starbursts

          foreach y in starbursts {% check for stars

            ifnumx=y% a star is born!

                node[fill=white,draw,starburst,inner sep=1pt] at (c) {$x$};

                globalnotfoundfalse% need global as inside a loop

            fi

          }

          ifnotfound% we have not printed a node yet

        node[fill=white,draw,circle,inner sep=1pt] at (c) {$x$};

          fi

        fi

        coordinate (b) at (c);

    };

  end{tikzpicture}



end{document}