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A262411
Lexicographically earliest sequence of distinct terms such that the ternary representations of two consecutive terms overlap.
7
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
1,2
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)).
EXAMPLE
. 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 )
PROG
(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
CROSSREFS
Cf. A262323, A030341, A007089, A262412 (ternary conversion), A262429 (inverse), A262435 (fixed points).
Cf. A262460.
Sequence in context: A099816 A237273 A272025 * A280488 A250072 A099120
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Sep 22 2015
STATUS
approved