mjhjmtu

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
usepackagestix
usepackagetikz
usetikzlibraryshapes.geometric
usetikzlibrarycalc
usepackagepifont
usepackagewasysym
usepackagegraphicx

begindocument
hspace0pt vfill
begincenter
 newcountercntRoot
 begintikzpicture
 coordinate (a) at (0,0);
 coordinate (b) at (0:1);
 foreach x in 1,...,100%
 coordinate (c) at ($(b)!0.9cm!270:(a)$);
 setcountercntRootx
 addtocountercntRoot1
 node[fill=white,draw,circle,inner sep=1pt] at (c)
 $thecntRoot$;
 coordinate (b) at (c);
 ;
 endtikzpicture
 endcenter
vfill
enddocument

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
usepackagestix
usepackagetikz
usetikzlibraryshapes,shapes.geometric,calc
usepackagepifont
usepackagewasysym
usepackagegraphicx
newififnotfound% to mark the stars as we print them
newcommandstarbursts3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99
begindocument

 begintikzpicture
 coordinate (a) at (0,0);
 coordinate (b) at (0:1);
 foreach x in 1,...,100%
 coordinate (c) at ($(b)!0.9cm!270:(a)$);
 pgfmathparseint(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);
 ;
 endtikzpicture

enddocument

EDIT

Here's a LaTeX3 version. The code is much neater but it is also slower in the sense that my laptop returns the following timings:

tikz: real 2.436 user 2.136 sys 0.281 pcpu 99.18

tikz: real 2.479 user 2.169 sys 0.294 pcpu 99.34

expl: real 2.557 user 2.250 sys 0.293 pcpu 99.45

expl: real 2.552 user 2.238 sys 0.301 pcpu 99.49

The output is the same as above. Here's the revised code:

documentclass[parskip]scrartcl
usepackage[margin=15mm]geometry
usepackagestix
usepackagetikz
usetikzlibraryshapes,shapes.geometric,calc
usepackagepifont
usepackagewasysym
usepackagegraphicx

tikzset
 mynode/.style = fill=white,draw,inner sep=1pt

usepackageexpl3
ExplSyntaxOn
clist_new:N l_starbursts
clist_set:Nn l_starbursts 3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99
newcommandSetNode[1]
 int_compare:nTF int_mod:nn #1 5 = 0 
 tikzsetmynode/.append~style=regular~polygon, regular~polygon~sides=5
 
 clist_if_in:NoTF l_starbursts #1
 tikzsetmynode/.append~style=starburst
 tikzsetmynode/.append~style=circle
 

cs_generate_variant:Nn clist_if_in:NnTF noTF
ExplSyntaxOff

newififnotfound% to mark the stars as we print them
begindocument

 begintikzpicture
 coordinate (a) at (0,0);
 coordinate (b) at (0:1);
 foreach x in 1,...,100%
 coordinate (c) at ($(b)!0.9cm!270:(a)$);
 SetNodex
 node[mynode] at (c) $x$;
 coordinate (b) at (c);
 ;
 endtikzpicture

enddocument

EDIT II

Here is a third "plain TeX" approach following jfbu's suggestion and where the stars take precedence over the hexagons (unlike above, as pointed out by sgmoye in the comments). I switched to plain TeX because, surprisingly, using LaTeX3 sequences in a similar fashion led to slower code. Perhaps clists would be better? It could also be that the first solution draws the nodes directly whereas solutions II and III use some tikzset... trickery. Anyway, here is the code:

documentclass[parskip]scrartcl
usepackage[margin=15mm]geometry
usepackagestix
usepackagetikz
usetikzlibraryshapes,shapes.geometric,calc
usepackagepifont
usepackagewasysym
usepackagegraphicx

tikzset
 mynode/.style = fill=white,draw,inner sep=1pt

newcommandstarbursts3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99
defsetnextstar#1,#2!%
 ifrelaxdetokenize#1relaxgdefnextstar200elsegdefnextstar#1gdefstarbursts#2fi%

expandaftersetnextstarstarbursts,,!

newcommandSetNode[1]
 ifnum#1=nextstar
 tikzsetmynode/.append style=starburst
 expandaftersetnextstarstarbursts!
 else
 pgfmathparseint(mod(x,5))
 ifnumpgfmathresult=0
 tikzsetmynode/.append style=regular polygon, regular polygon sides=5
 else
 tikzsetmynode/.append style=circle
 fi
 fi

begindocument

 begintikzpicture
 coordinate (a) at (0,0);
 coordinate (b) at (0:1);
 foreach x in 1,...,100%
 coordinate (c) at ($(b)!0.9cm!270:(a)$);
 SetNodex
 node[mynode] at (c) $x$;
 coordinate (b) at (c);
 ;
 endtikzpicture

enddocument

The output is slightly different in that 80 now has a star.