

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
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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!  (n1)! for 2 <= n <= 10. Then the sum is telescopic, yielding 10!  1!. Adding the 2 initial terms we get the result.) The smallest 10digit 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



