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

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, 29, 28, 27, 30, 31, 32, 34, 33, 37, 35, 38, 39, 36, 40, 41, 42, 43, 44, 46, 45, 49, 47, 50, 48, 52, 51, 54, 53, 55, 56, 57, 59, 58, 60, 61, 62, 63, 65, 64, 68, 66

Offset: 1

Author

Reinhard Zumkeller, Sep 22 2015

Keywords

• nonn
• base

Comments

Suggested by Paul Tek's A262323;

two numbers are overlapping if a nonempty prefix of one equals a suffix of the other;

permutation of the natural numbers with inverse A262429;

A262412(n) = A007089(a(n)).

Examples

			.   n | a(n) | A262412(n)           n | a(n) | A262412(n)
. ----+------+-----------         ----+------+-------------
.                                 (25 |   26 |         222 )
.   1 |    1 |   1                 26 |   24 |          220
.   2 |    3 |   10                27 |   29 |       1002
.   3 |    4 |  11                 28 |   28 |    1001
.   4 |    5 |   12                29 |   27 |       1000
.   5 |    2 |    2                30 |   30 |     1010
.   6 |    6 |    20               31 |   31 |  1011
.   7 |    8 |   22                32 |   32 |     1012
.   8 |    7 |    21               33 |   34 |  1021
.   9 |    9 |     100             34 |   33 |     1020
.  10 |   10 |   101               35 |   37 |  1101
.  11 |   11 |     102             36 |   35 |     1022
.  12 |   12 |    110              37 |   38 |    1102
.  13 |   13 |   111               38 |   39 |   1110
.  14 |   14 |    112              39 |   36 |    1100
.  15 |   15 |     120             40 |   40 |  1111
.  16 |   16 |   121               41 |   41 |   1112
.  17 |   17 |     122             42 |   42 |    1120
.  18 |   18 |       200           43 |   43 | 1121
.  19 |   20 |     202             44 |   44 |    1122
.  20 |   19 |       201           45 |   46 | 1201
.  21 |   23 |     212             46 |   45 |    1200
.  22 |   21 |       210           47 |   49 | 1211
.  23 |   25 |      221            48 |   47 |    1202
.  24 |   22 |       211           49 |   50 |  1212
.  25 |   26 |     222             50 |   48 |    1210  .
. (26 |   24 |      220 )
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A262323, A030341, A007089, A262412 (ternary conversion), A262429 (inverse), A262435 (fixed points).

Cf. A262460.

Programs

Haskell

import Data.List (inits, tails, intersect, delete, genericIndex)
a262411 n = genericIndex a262411_list (n - 1)
a262411_list = 1 : f [1] (drop 2 a030341_tabf) where
   f xs tss = g tss where
     g (ys:yss) | null (intersect its $ tail $ inits ys) &&
                  null (intersect tis $ init $ tails ys) = g yss
                | otherwise = (foldr (\t v -> 3 * v + t) 0 ys) :
                              f ys (delete ys tss)
     its = init $ tails xs; tis = tail $ inits xs