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Characteristic function of numbers having distinct digits in their decimal representation.
19

%I #21 Feb 13 2013 04:38:41

%S 1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,

%T 1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,

%U 1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,1,1,1

%N Characteristic function of numbers having distinct digits in their decimal representation.

%C a(A010784(n)) = 1; a(A109303(n)) = 0;

%C first differences of A178787.

%C a(n) <= A196368(n).

%C a(n) = 0 for n > 9*9!. - _Hieronymus Fischer_, Feb 02 2013

%H R. Zumkeller, <a href="/A178788/b178788.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Digit.html">Digit</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = 0^(A055642(n)-A043537(n)).

%t lst = {}; Do[If[Select[Tally[IntegerDigits[n]][[All, 2]], # > 1 &] == {}, AppendTo[lst, 1], AppendTo[lst, 0]], {n, 0, 104}]; lst (* _Arkadiusz Wesolowski_, May 10 2012 *)

%o (Haskell)

%o import Data.List (nub)

%o a178788 n = fromEnum $ nub (show n) == show n

%o -- _Reinhard Zumkeller_, Sep 25 2011

%K base,nonn

%O 0,1

%A _Reinhard Zumkeller_, Jun 30 2010