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