Hmm. Golf eh? 88 strokes. First 99 19 values. Bleh. 99 takes too long.

Works under linux, Swap double and single quotes for Windows.

         1         2         3         4         5         6         7         8         9
123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890

perl -E'$_=1;while(++$t<19){say;my@a;push@a,length$1,$2 while/((\d)\2*
+)/g;$_=join"",@a}'
[download]

Update 79 75 73 strokes

         1         2         3         4         5         6         7         8
12345678901234567890123456789012345678901234567890123456789012345678901234567890

perl -E'for(0..19){say$_=$t//1;$t="";$t.=(length$1).$2 while/((.)\2*)/
+g}'
[download]