A178788 Characteristic function of numbers having distinct digits in their decimal representation.

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Jun 30 2010

Keywords

• base
• nonn

Comments

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

first differences of A178787.

a(n) <= A196368(n).

a(n) = 0 for n > 9*9!. - Hieronymus Fischer, Feb 02 2013

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000
• Michael De Vlieger, Plot a(n) at (x,y) = (n mod 1000, -floor(n/1000)), n = 1..10^6, where black represents a(n) = 1 and white represents a(n) = 0.
• Eric Weisstein's World of Mathematics, Digit
• Index entries for characteristic functions

Programs

Haskell

import Data.List (nub)
a178788 n = fromEnum $ nub (show n) == show n
-- Reinhard Zumkeller, Sep 25 2011

Mathematica

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 *)

Formula

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