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%I #14 Jan 02 2018 15:54:46
%S 0,1,10,102,120,201,210,1023,1032,1203,1230,1302,1320,2013,2031,2103,
%T 2130,2301,2310,3012,3021,3102,3120,3201,3210,10234,10243,10324,10342,
%U 10423,10432,12034,12043,12304,12340,12403,12430,13024,13042,13204,13240,13402,13420,14023
%N Starting with a(1) = 0, a(2) = 1, a(n) = smallest nonnegative integer that shares all digits with previous terms. No repeated digits are allowed.
%C With the restriction that no repeated digits are allowed, the sequence is finite and contains 10! + 1 terms. (Proof: The number of terms of length n is equal to n! - (n-1)! for 2 <= n <= 10. Then the sum is telescopic, yielding 10! - 1!. Adding the 2 initial terms we get the result.) The smallest 10-digit term is 1023456789 and the last term of the sequence is 9876543210.
%t Nest[Function[a, Append[a, Block[{k = Last@ a + 1}, While[Nand[Union@ Tally[#][[All, -1]] == {1}, Complement[Union@ Flatten@ Map[IntegerDigits, a], #] == {}] &@ IntegerDigits@ k, k++]; k]]], {0, 1}, 42] (* _Michael De Vlieger_, Dec 24 2017 *)
%Y Cf. A199168.
%K nonn,base
%O 1,3
%A _Enrique Navarrete_, Dec 24 2017
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