A190132 - OEIS

%I #19 Feb 16 2025 08:33:14

%S 1,12,144,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,

%T 145,1740,1741,1742,1743,1744,1745,1746,1747,1748,1749,1750,1751,146,

%U 1752,1753,1754,1755,1756,1757,1758,1759,1760,1761,1762,1763,147,1764,1765

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

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

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

%H Reinhard Zumkeller, <a href="/A190132/b190132.txt">Table of n, a(n) for n = 1..10000</a> (full sequence)

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LexicographicOrder.html">Lexicographic Order</a>

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lexicographical_order">Lexicographical order</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Duodecimal">Duodecimal</a>

%e a(13) = 1737 -> 1009 [doz];

%e a(14) = 1738 -> 100A [doz];

%e a(15) = 1739 -> 100B [doz];

%e a(16) =  145 -> 101  [doz];

%e a(17) = 1740 -> 1010 [doz];

%e a(18) = 1741 -> 1011 [doz];

%e largest term a(9026) = 10000 -> 5282 [doz];

%e last term a(10000) = 1727 -> BBB [doz], largest term lexicographically.

%o (Haskell)

%o import Data.Ord (comparing)

%o import Data.List (sortBy)

%o import Numeric (showIntAtBase)

%o import Data.Char (intToDigit)

%o a190132 n = a190132_list !! (n-1)

%o a190132_list =

%o    sortBy (comparing (flip (showIntAtBase 12 intToDigit) "")) [1..10000]

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

%K nonn,base,fini,full,changed

%O 1,2

%A _Reinhard Zumkeller_, May 06 2011