[math-fun] Shortest sequence = add two terms, share no digit

Hello math-fun, this sequence of integers (computed by Olivier Miakinen) has those properties: - starts with "1"; - increases monotonically; - sum of two consecutive terms doesn't share any digit with the two sumands; - stops after 29 terms. 1 2 9 11 22 93 111 222 933 1111 2222 9333 11111 22222 93333 111111 222222 933333 1111111 2222222 9333333 11111111 22222222 93333333 111111111 331393339 339112349 368595421 409182356 ** END ** Question: What would be the shortest such sequence? Best, É.