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A262323 Lexicographically earliest sequence of distinct terms such that the decimal representations of two consecutive terms overlap. 9

%I

%S 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,

%T 42,27,7,17,51,18,8,28,52,29,9,19,61,36,43,34,40,44,45,50,35,53,37,63,

%U 38,73,39,83,48,54,46,60,56,55,57,65,58,75,47,64,49,74

%N Lexicographically earliest sequence of distinct terms such that the decimal representations of two consecutive terms overlap.

%C Two terms are said to overlap:

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

%C - 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).

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

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

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

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

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

%H Paul Tek, <a href="/A262323/b262323.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Tek, <a href="/A262323/a262323.pl.txt">PERL program for this sequence</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms of the sequence are:

%e +----+---------+

%e | n | a(n) |

%e +----+---------+

%e | 1 | 1 |

%e | 2 | 10 |

%e | 3 | 11 |

%e | 4 | 12 |

%e | 5 | 2 |

%e | 6 | 20 |

%e | 7 | 22 |

%e | 8 | 21 |

%e | 9 | 13 |

%e | 10 | 3 |

%e | 11 | 23 |

%e | 12 | 30 |

%e | 13 | 33 |

%e | 14 | 31 |

%e | 15 | 14 |

%e | 16 | 4 |

%e | 17 | 24 |

%e | 18 | 32 |

%e | 19 | 25 |

%e | 20 | 5 |

%e +----+---------+

%o (Perl) See Links section.

%o (Haskell)

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

%o a262323 n = a262323_list !! (n-1)

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

%o f xs zss = g zss where

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

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

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

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

%o -- _Reinhard Zumkeller_, Sep 21 2015

%Y Cf. A076654, A262255, A262283.

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

%K nonn,look,base,nice

%O 1,2

%A _Paul Tek_, Sep 19 2015

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Last modified July 12 00:27 EDT 2020. Contains 335658 sequences. (Running on oeis4.)