cp's OEIS Frontend

A120005 Smallest number containing exactly n distinct numbers in its decimal representation.

%I A120005 #9 Aug 17 2025 17:36:38
%S A120005 0,11,10,100,102,120,1012,1023,1120,1230,10123,10234,11203,11230,
%T A120005 12340,101234,102345,111230,112130,112340,123450,1012345,1023456,
%U A120005 1112130,1112340,1121340,1123450,1234560
%N A120005 Smallest number containing exactly n distinct numbers in its decimal representation.
%C A120005 A000030(a(n)) = 1 for n > 1;
%C A120005 A120004(a(n)) = n and A120004(m) < n for m < a(n).
%e A120005 Illustration of initial values:
%e A120005 .   n |   a(n) ... and n-1 proper substrings
%e A120005 . ----+----------------------------------------------------
%e A120005 .   1 |     0
%e A120005 .   2 |    11    1
%e A120005 .   3 |    10    1    0
%e A120005 .   4 |   100   10    1   0
%e A120005 .   5 |   102   10    2   1   0
%e A120005 .   6 |   120   20   12   2   1   0
%e A120005 .   7 |  1012  101   12  10   2   1  0
%e A120005 .   8 |  1023  102   23  10   3   2  1  0
%e A120005 .   9 |  1120  120  112  20  12  11  2  1  0
%e A120005 .  10 |  1230  230  123  30  23  12  3  2  1  0
%e A120005 .  11 | 10123 1012  123 101  23  12 10  3  2  1 0
%e A120005 .  12 | 10234 1023  234 102  34  23 10  4  3  2 1 0
%e A120005 .  13 | 11203 1203 1120 203 120 112 20 12 11  3 2 1 0
%e A120005 .  14 | 11230 1230 1123 230 123 112 30 23 12 11 3 2 1 0
%e A120005 .  15 | 12340 2340 1234 340 234 123 40 34 23 12 4 3 2 1 0 .
%o A120005 (Haskell)
%o A120005 import Data.List (isInfixOf, elemIndex)
%o A120005 import Data.Maybe (fromJust)
%o A120005 a120005 = fromJust . (`elemIndex` a120004_list)
%o A120005 -- _Reinhard Zumkeller_, Jul 16 2012
%K A120005 nonn,base
%O A120005 1,2
%A A120005 _Reinhard Zumkeller_, Jun 15 2006
%E A120005 a(1) changed from 1 to 0 by _Zak Seidov_, May 30 2010