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A190128 Numbers 1 through 10000 sorted lexicographically in ternary representation.

%I A190128 #16 Feb 16 2025 08:33:14
%S A190128 1,3,9,27,81,243,729,2187,6561,6562,6563,2188,6564,6565,6566,2189,
%T A190128 6567,6568,6569,730,2190,6570,6571,6572,2191,6573,6574,6575,2192,6576,
%U A190128 6577,6578,731,2193,6579,6580,6581,2194,6582,6583,6584,2195,6585,6586,6587,244
%N A190128 Numbers 1 through 10000 sorted lexicographically in ternary representation.
%C A190128 A190129 = inverse permutation: a(A190129(n)) = A190129(a(n)) = n;
%C A190128 a(n) <> n for n > 1.
%H A190128 Reinhard Zumkeller, <a href="/A190128/b190128.txt">Table of n, a(n) for n = 1..10000</a> (full sequence)
%H A190128 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LexicographicOrder.html">Lexicographic Order</a>
%H A190128 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ternary.html">Ternary</a>
%H A190128 Wikipedia, <a href="http://en.wikipedia.org/wiki/Lexicographical_order">Lexicographical order</a>
%H A190128 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ternary_numeral_system">Ternary numeral system</a>
%e A190128 a(12) = 2188 -> 10000001  [tern];
%e A190128 a(13) = 6564 -> 100000010 [tern];
%e A190128 a(14) = 6565 -> 100000011 [tern];
%e A190128 a(15) = 6566 -> 100000012 [tern];
%e A190128 a(16) = 2189 -> 10000002  [tern];
%e A190128 a(17) = 6567 -> 100000020 [tern];
%e A190128 a(18) = 6568 -> 100000021 [tern];
%e A190128 a(19) = 6569 -> 100000022 [tern];
%e A190128 a(20) =  730 -> 1000001   [tern];
%e A190128 a(21) = 2190 -> 10000010  [tern];
%e A190128 largest term a(5164) = 10000 -> 111201101 [tern];
%e A190128 last term a(10000) = 6560 -> 22222222 [tern], largest term lexicographically.
%o A190128 (Haskell)
%o A190128 import Data.Ord (comparing)
%o A190128 import Data.List (sortBy)
%o A190128 a190128 n = a190128_list !! (n-1)
%o A190128 a190128_list = sortBy (comparing (show . a007089)) [1..10000]
%Y A190128 Cf. A007089; A190126 (base 2), A190130 (base 8), A190016 (base 10), A190132 (base 12), A190134 (base 16).
%K A190128 nonn,base,fini,full
%O A190128 1,2
%A A190128 _Reinhard Zumkeller_, May 06 2011