A262412 -id:A262412

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A262411

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

+10
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

(list; graph; refs; listen; history; text; internal format)

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)).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

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.

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Sep 22 2015

STATUS

approved

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