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A262411 Lexicographically earliest sequence of distinct terms such that the ternary representations of two consecutive terms overlap.

%I A262411 #14 Dec 11 2015 21:54:15
%S A262411 1,3,4,5,2,6,8,7,9,10,11,12,13,14,15,16,17,18,20,19,23,21,25,22,26,24,
%T A262411 29,28,27,30,31,32,34,33,37,35,38,39,36,40,41,42,43,44,46,45,49,47,50,
%U A262411 48,52,51,54,53,55,56,57,59,58,60,61,62,63,65,64,68,66
%N A262411 Lexicographically earliest sequence of distinct terms such that the ternary representations of two consecutive terms overlap.
%C A262411 Suggested by Paul Tek's A262323;
%C A262411 two numbers are overlapping if a nonempty prefix of one equals a suffix of the other;
%C A262411 permutation of the natural numbers with inverse A262429;
%C A262411 A262412(n) = A007089(a(n)).
%H A262411 Reinhard Zumkeller, <a href="/A262411/b262411.txt">Table of n, a(n) for n = 1..10000</a>
%H A262411 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A262411 .   n | a(n) | A262412(n)           n | a(n) | A262412(n)
%e A262411 . ----+------+-----------         ----+------+-------------
%e A262411 .                                 (25 |   26 |         222 )
%e A262411 .   1 |    1 |   1                 26 |   24 |          220
%e A262411 .   2 |    3 |   10                27 |   29 |       1002
%e A262411 .   3 |    4 |  11                 28 |   28 |    1001
%e A262411 .   4 |    5 |   12                29 |   27 |       1000
%e A262411 .   5 |    2 |    2                30 |   30 |     1010
%e A262411 .   6 |    6 |    20               31 |   31 |  1011
%e A262411 .   7 |    8 |   22                32 |   32 |     1012
%e A262411 .   8 |    7 |    21               33 |   34 |  1021
%e A262411 .   9 |    9 |     100             34 |   33 |     1020
%e A262411 .  10 |   10 |   101               35 |   37 |  1101
%e A262411 .  11 |   11 |     102             36 |   35 |     1022
%e A262411 .  12 |   12 |    110              37 |   38 |    1102
%e A262411 .  13 |   13 |   111               38 |   39 |   1110
%e A262411 .  14 |   14 |    112              39 |   36 |    1100
%e A262411 .  15 |   15 |     120             40 |   40 |  1111
%e A262411 .  16 |   16 |   121               41 |   41 |   1112
%e A262411 .  17 |   17 |     122             42 |   42 |    1120
%e A262411 .  18 |   18 |       200           43 |   43 | 1121
%e A262411 .  19 |   20 |     202             44 |   44 |    1122
%e A262411 .  20 |   19 |       201           45 |   46 | 1201
%e A262411 .  21 |   23 |     212             46 |   45 |    1200
%e A262411 .  22 |   21 |       210           47 |   49 | 1211
%e A262411 .  23 |   25 |      221            48 |   47 |    1202
%e A262411 .  24 |   22 |       211           49 |   50 |  1212
%e A262411 .  25 |   26 |     222             50 |   48 |    1210  .
%e A262411 . (26 |   24 |      220 )
%o A262411 (Haskell)
%o A262411 import Data.List (inits, tails, intersect, delete, genericIndex)
%o A262411 a262411 n = genericIndex a262411_list (n - 1)
%o A262411 a262411_list = 1 : f [1] (drop 2 a030341_tabf) where
%o A262411    f xs tss = g tss where
%o A262411      g (ys:yss) | null (intersect its $ tail $ inits ys) &&
%o A262411                   null (intersect tis $ init $ tails ys) = g yss
%o A262411                 | otherwise = (foldr (\t v -> 3 * v + t) 0 ys) :
%o A262411                               f ys (delete ys tss)
%o A262411      its = init $ tails xs; tis = tail $ inits xs
%Y A262411 Cf. A262323, A030341, A007089, A262412 (ternary conversion), A262429 (inverse), A262435 (fixed points).
%Y A262411 Cf. A262460.
%K A262411 nonn,base
%O A262411 1,2
%A A262411 _Reinhard Zumkeller_, Sep 22 2015