[math-fun] ACRONYMS : A Common Representation Of Names You Must Shorten

Hello SeqFans & Math-Fun, If those two seq. are of interest, could someone help in providing more terms? ------------------------ First digit of a(n) is given by the succession of digits in S [a(n+1) is the smallest available integer not yet present in S]: S= 0,1,2,3,4,5,6,7,8,9,11,12,13,21,14,31,22,15,16,41,32,17,23,24,17,51,18,61... ------------------------ First digit of a(n) is given by the succession of digits in S [S is monotonicaly increasing]: S= 0,1,2,3,4,5,6,7,8,9,11,12,13,21,111,311,2111,11111,11112,11113,11114,31111,... ------------------------ Best, É.