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A263563 A self-describing sequence: when the sequence is read as a string of decimal digits, a(n) can be read from position n (ignoring leading zeros). This sequence is the lexicographically earliest sequence of distinct terms with this property. 3

%I #22 Apr 25 2016 12:00:17

%S 1,2,3,4,5,6,7,8,9,10,11,110,100,12,120,1200,20,13,130,1300,30,14,140,

%T 1400,40,15,150,1500,50,16,160,1600,60,17,170,1700,70,18,180,1800,80,

%U 19,190,1900,90,21,210,2100,1000,22,220,2200,22000,200,23,230,2300

%N A self-describing sequence: when the sequence is read as a string of decimal digits, a(n) can be read from position n (ignoring leading zeros). This sequence is the lexicographically earliest sequence of distinct terms with this property.

%C Leading zeros that may appear while reading a(n) arise from non-leading zeros in some previous term, and are ignored.

%C The table in the Example section makes the definition clearer.

%C This sequence is conjectured to be a permutation of natural numbers, with putative inverse A263564.

%H Paul Tek, <a href="/A263563/b263563.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Tek, <a href="/A263563/a263563.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 following table depicts the first few terms:

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

%e | n | a(n) | a(n) in situation with leading 0s |

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

%e | 1 | 1 | 1 |

%e | 2 | 2 | 2 |

%e | 3 | 3 | 3 |

%e | 4 | 4 | 4 |

%e | 5 | 5 | 5 |

%e | 6 | 6 | 6 |

%e | 7 | 7 | 7 |

%e | 8 | 8 | 8 |

%e | 9 | 9 | 9 |

%e | 10 | 10 | 10 |

%e | 11 | 11 | 011 |

%e | 12 | 110 | 110 |

%e | 13 | 100 | 100 |

%e | 14 | 12 | 0012 |

%e | 15 | 120 | 0120 |

%e | 16 | 1200 | 1200 |

%e | 17 | 20 | 200 |

%e | 18 | 13 | 0013 |

%e | 19 | 130 | 0130 |

%e | 20 | 1300 | 1300 |

%e | 21 | 30 | 300 |

%e | 22 | 14 | 0014 |

%e | 23 | 140 | 0140 |

%e | 24 | 1400 | 1400 |

%e | 25 | 40 | 400 |

%e | 26 | 15 | 0015 |

%e | 27 | 150 | 0150 |

%e | 28 | 1500 | 1500 |

%e | 29 | 50 | 500 |

%e | 30 | 16 | 0016 |

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

%e Comments from _N. J. A. Sloane_, Jan 18 2016 (Start): After a(9)=9, the smallest possible choice for a(10) is the first number that has not yet appeared, which is 10. There is no contradiction, so we take a(10)=10.

%e Now the smallest number that has not yet appeared is 11, and we can achieve a(11)=11 by making the string of digits starting at the 11th place read 011.

%e Now the string of digits starting at the 12th pace is 11..., and the smallest candidate of that form is 110, which gives a(12)=110.

%e And so on. (End)

%o (Perl) See Links section.

%Y Cf. A263443, A263564.

%K nonn,base,look,nice

%O 1,2

%A _Paul Tek_, Oct 21 2015

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)