From the smallest seed
Challenge
It's a bootstrapping challenge this time! Write a full program that, once run, writes the source code of another program that in turn, once run, writes the source code for another program, ad infinitum.
However, you can't just do a quine. The length of each program must tend toward infinity as the sequence continues. While you can have programs that create smaller programs within the sequence, the overall trend must tend towards infinity.
Your score is the length of the initial program. This is code golf, so the lowest score wins!
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Zsh, 61 bytes
n=2;s=s=%q\;printf\ n=\$n\$n\\\;\$s\ \$s;printf n=$n$n\;$s $sA trivial modification of this quine: s=s=%q\;printf\ \$s\ \$s;printf $s $s. n goes from 2 to 22 to 2222.
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