OFFSET

1,3

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.

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 *)

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Enrique Navarrete, Dec 24 2017

STATUS

approved