A190132 Numbers 1 through 10000 sorted lexicographically in duodecimal representation (base 12).

1, 12, 144, 1728, 1729, 1730, 1731, 1732, 1733, 1734, 1735, 1736, 1737, 1738, 1739, 145, 1740, 1741, 1742, 1743, 1744, 1745, 1746, 1747, 1748, 1749, 1750, 1751, 146, 1752, 1753, 1754, 1755, 1756, 1757, 1758, 1759, 1760, 1761, 1762, 1763, 147, 1764, 1765

Offset: 1

Author

Reinhard Zumkeller, May 06 2011

Keywords

• nonn
• base
• fini
• full

Comments

A190133 = inverse permutation: a(A190133(n)) = A190133(a(n)) = n;

a(n) <> n for n > 1.

Examples

			a(13) = 1737 -> 1009 [doz];
a(14) = 1738 -> 100A [doz];
a(15) = 1739 -> 100B [doz];
a(16) =  145 -> 101  [doz];
a(17) = 1740 -> 1010 [doz];
a(18) = 1741 -> 1011 [doz];
largest term a(9026) = 10000 -> 5282 [doz];
last term a(10000) = 1727 -> BBB [doz], largest term lexicographically.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (full sequence)
• Eric Weisstein's World of Mathematics, Lexicographic Order
• Eric Weisstein's World of Mathematics, Duodecimal
• Wikipedia, Lexicographical order
• Wikipedia, Duodecimal

Crossrefs

Cf. A190126 (base 2), A190128 (base 3), A190130 (base 8), A190016 (base 10), A190134 (base 16).

Programs

Haskell

import Data.Ord (comparing)
import Data.List (sortBy)
import Numeric (showIntAtBase)
import Data.Char (intToDigit)
a190132 n = a190132_list !! (n-1)
a190132_list =
   sortBy (comparing (flip (showIntAtBase 12 intToDigit) "")) [1..10000]