Conway Look-and-Say, as a Perl one liner

$ perl -e '$x=1;for(;;){print"$x\n";$x=~s/((\d)\2*)/length($1).$2/eg;}' | head

1
11
21
1211
111221
312211
13112221
1113213211
31131211131221
13211311123113112211

See definition. See also Abigail's test for primality.