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A262323 Lexicographically earliest sequence of distinct terms such that the decimal representations of two consecutive terms overlap. 8
1, 10, 11, 12, 2, 20, 22, 21, 13, 3, 23, 30, 33, 31, 14, 4, 24, 32, 25, 5, 15, 41, 16, 6, 26, 42, 27, 7, 17, 51, 18, 8, 28, 52, 29, 9, 19, 61, 36, 43, 34, 40, 44, 45, 50, 35, 53, 37, 63, 38, 73, 39, 83, 48, 54, 46, 60, 56, 55, 57, 65, 58, 75, 47, 64, 49, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Two terms are said to overlap:

- if the decimal representation of one term is contained in the decimal representation of the other term (for example, 12 and 2 overlap),

- or if, for some k>0, the first k decimal digits (without leading zero) of one term correspond to the k last decimal digits of the other term (for example, 1017 and 1101 overlap).

This sequence is a permutation of the positive integers, with inverse A262255.

The first overlap involving 1 digit occurs between a(1)=1 and a(2)=10.

The first overlap involving 2 digits occurs between a(108)=100 and a(109)=110.

The first overlap involving 3 digits occurs between a(1039)=1017 and a(1040)=1101.

The first overlap involving 4 digits occurs between a(10584)=10212 and a(10585)=11021.

LINKS

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, PERL program for this sequence

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The first terms of the sequence are:

+----+---------+

| n  | a(n)    |

+----+---------+

|  1 |  1      |

|  2 |  10     |

|  3 | 11      |

|  4 |  12     |

|  5 |   2     |

|  6 |   20    |

|  7 |  22     |

|  8 |   21    |

|  9 |    13   |

| 10 |     3   |

| 11 |    23   |

| 12 |     30  |

| 13 |    33   |

| 14 |     31  |

| 15 |      14 |

| 16 |       4 |

| 17 |      24 |

| 18 |     32  |

| 19 |      25 |

| 20 |       5 |

+----+---------+

PROG

(Perl) See Links section.

(Haskell)

import Data.List (inits, tails, intersect, delete)

a262323 n = a262323_list !! (n-1)

a262323_list = 1 : f "1" (map show [2..]) where

   f xs zss = g zss where

     g (ys:yss) | null (intersect its $ tail $ inits ys) &&

                  null (intersect tis $ init $ tails ys) = g yss

                | otherwise = (read ys :: Int) : f ys (delete ys zss)

     its = init $ tails xs; tis = tail $ inits xs

-- Reinhard Zumkeller, Sep 21 2015

CROSSREFS

Cf. A076654, A262255, A262283.

Cf. A262367 (fixed points), A262411 (ternary version), A262460 (hexadecimal version).

Sequence in context: A184992 A162501 A286890 * A262412 A333722 A299981

Adjacent sequences:  A262320 A262321 A262322 * A262324 A262325 A262326

KEYWORD

nonn,look,base,nice

AUTHOR

Paul Tek, Sep 19 2015

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)