A297062 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.

0, 1, 10, 102, 120, 201, 210, 1023, 1032, 1203, 1230, 1302, 1320, 2013, 2031, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210, 10234, 10243, 10324, 10342, 10423, 10432, 12034, 12043, 12304, 12340, 12403, 12430, 13024, 13042, 13204, 13240, 13402, 13420, 14023

Offset: 1

Author

Enrique Navarrete, Dec 24 2017

Keywords

• nonn
• base

Comments

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.

Crossrefs

Cf. A199168.

Programs

Mathematica

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 *)