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Lexicographically earliest permutation of the natural numbers such that in decimal representation d(n) is contained in a(n), where d is the digit sequence of the concatenation of the a-sequence, cf. A247149.
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%I #15 Jan 02 2023 12:30:50

%S 0,1,2,3,4,5,6,7,8,9,10,20,12,30,11,21,13,40,14,15,22,16,17,23,24,50,

%T 18,34,19,25,26,27,31,36,41,37,28,32,29,42,35,60,51,38,33,43,61,39,52,

%U 45,62,46,72,47,53,71,63,56,44,81,73,57,82,48,83,92,102

%N Lexicographically earliest permutation of the natural numbers such that in decimal representation d(n) is contained in a(n), where d is the digit sequence of the concatenation of the a-sequence, cf. A247149.

%C By definition: A247149(n) is contained in a(n).

%H Reinhard Zumkeller, <a href="/A247143/b247143.txt">Table of n, a(n) for n = 0..10000</a>

%H Éric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-November/013974.html">The a(n)th digit of S is present in a(n)</a>, SeqFan list, Nov 20 2014.

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

%e . n | d(n) | a(n) | n | d(n) | a(n) | n | d(n) | a(n) |

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

%e . 10 | 1 | 10 | 100 | 7 | 78 | 1000 | 5 | 885 |

%e . 11 | 0 | 20 | 101 | 1 | 101 | 1001 | 1 | 1040 |

%e . 12 | 2 | 12 | 102 | 6 | 69 | 1002 | 6 | 868 |

%e . 13 | 0 | 30 | 103 | 3 | 133 | 1003 | 3 | 1053 |

%e . 14 | 1 | 11 | 104 | 5 | 105 | 1004 | 3 | 1063 |

%e . 15 | 2 | 21 | 105 | 6 | 86 | 1005 | 5 | 895 |

%e . 16 | 3 | 13 | 106 | 4 | 114 | 1006 | 3 | 1073 |

%e . 17 | 0 | 40 | 107 | 4 | 124 | 1007 | 4 | 945 |

%e . 18 | 1 | 14 | 108 | 8 | 80 | 1008 | 6 | 869 |

%e . 19 | 1 | 15 | 109 | 1 | 106 | 1009 | 5 | 905 |

%e . 20 | 2 | 22 | 110 | 7 | 79 | 1010 | 1 | 1041 |

%e . 21 | 1 | 16 | 111 | 3 | 134 | 1011 | 7 | 876 |

%e . 22 | 1 | 17 | 112 | 5 | 115 | 1012 | 3 | 1083 |

%e . 23 | 3 | 23 | 113 | 7 | 87 | 1013 | 4 | 946 | .

%o (Haskell)

%o import Data.List (delete, find); import Data.Maybe (fromJust)

%o a247143 n = a247143_list !! n

%o a247143_list = [0..10] ++ f 11 (map show [11..]) where

%o f x zss = (read ys :: Int) : f (x + 1) (delete ys zss) where

%o ys = fromJust $ find (elem $ ds !! x) zss

%o ds = concatMap show a247143_list

%Y Cf. A247144 (inverse), A247149 (digits), A247167 (fixed points).

%K nonn,base

%O 0,3

%A _Eric Angelini_ and _Reinhard Zumkeller_, Nov 20 2014