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recursive numbering


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found this interesting idea on the web over at xkcd.

<number> := <prime>
<number> := <composite>
<composite> := <number> <number>
<prime> := 1
<prime> := 'p' '(' <composite> ')'
<prime> := 'p' <prime>

then the first 20 numbers are:

1

p1

pp1

p1p1

ppp1

pp1p1

p(p1p1)

p1p1p1

pp1pp1

p1ppp1

pppp1

p1p1pp1

p(p1pp1)

p1p(p1p1)

pp1ppp1

p1p1p1p1

pp(p1p1)

p1pp1pp1

p(p1p1p1)

p1p1ppp1

can you generate the next 20?

 

 

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