Hmm. Golf eh? 88 strokes. First 99 19 values. Bleh. 99 takes too long.
Works under linux, Swap double and single quotes for Windows.
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123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
perl -E'$_=1;while(++$t<19){say;my@a;push@a,length$1,$2 while/((\d)\2*
+)/g;$_=join"",@a}'
Update 79 75 73 strokes
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12345678901234567890123456789012345678901234567890123456789012345678901234567890
perl -E'for(0..19){say$_=$t//1;$t="";$t.=(length$1).$2 while/((.)\2*)/
+g}'
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