Hello SeqFan and Math-Fun, I guess this definition is better (for both seq.), sorry: First digit of a(n) is the a(n)th digit of S. Neil will add both seq. to the OEIS -- but more terms are still needed. Best, E.

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.