A212193 In ternary representation of n: a(n) = if n is pandigital then 3 else least digit not used.

1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2, 3, 2, 0, 0, 3, 0, 0, 1, 3, 1, 3, 0, 0, 1, 0, 0, 2, 2, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3, 2, 0, 0, 3, 0, 0, 3, 3, 3, 3, 0, 0, 3, 0, 0, 1, 3, 1, 3, 3, 3, 1, 3, 1, 3, 3, 3, 3, 0, 0, 3, 0, 0, 1, 3, 1, 3, 0, 0, 1, 0, 0, 2, 2, 3, 2, 2

Offset: 0

Author

Reinhard Zumkeller, May 04 2012

Keywords

• nonn
• base

Comments

a(A032924(n)) = 0; a(A081605(n)) <> 0;

a(A031944(n)) = 3; a(A154314(n)) <> 3.

Examples

			.   0 ->   '0':   a(0) = 1
.   1 ->   '1':   a(1) = 0
.   2 ->   '2':   a(2) = 0
.   3 ->  '10':   a(3) = 2
.   4 ->  '11':   a(4) = 0
.   5 ->  '12':   a(5) = 0
.   6 ->  '20':   a(6) = 1
.   7 ->  '21':   a(7) = 0
.   8 ->  '22':   a(8) = 0
.   9 -> '100':   a(9) = 2
.  10 -> '101':  a(10) = 2
.  11 -> '102':  a(11) = 3  <-- 11 is the smallest 3-pandigital number
.  12 -> '110':  a(12) = 2
.  13 -> '111':  a(13) = 0
.  14 -> '112':  a(14) = 0
.  15 -> '120':  a(15) = 3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Ternary
• Eric Weisstein's World of Mathematics, Pandigital Number
• Wikipedia, Ternary numeral system
• Wikipedia, Pandigital number

Crossrefs

Cf. A007089, A067898 (decimal).

Programs

Haskell

import Data.List (delete)
a212193 n = f n [0..3] where
   f x ys | x <= 2    = head $ delete x ys
          | otherwise = f x' $ delete d ys where (x',d) = divMod x 3