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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..44.

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

Cf. A199168.

Sequence in context: A309540 A039393 A199168 * A203569 A305712 A053041

Adjacent sequences:  A297059 A297060 A297061 * A297063 A297064 A297065

KEYWORD

nonn,base

AUTHOR

Enrique Navarrete, Dec 24 2017

STATUS

approved

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Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)