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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.

%I A263563 #22 Apr 25 2016 12:00:17
%S A263563 1,2,3,4,5,6,7,8,9,10,11,110,100,12,120,1200,20,13,130,1300,30,14,140,
%T A263563 1400,40,15,150,1500,50,16,160,1600,60,17,170,1700,70,18,180,1800,80,
%U A263563 19,190,1900,90,21,210,2100,1000,22,220,2200,22000,200,23,230,2300
%N 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.
%C A263563 Leading zeros that may appear while reading a(n) arise from non-leading zeros in some previous term, and are ignored.
%C A263563 The table in the Example section makes the definition clearer.
%C A263563 This sequence is conjectured to be a permutation of natural numbers, with putative inverse A263564.
%H A263563 Paul Tek, <a href="/A263563/b263563.txt">Table of n, a(n) for n = 1..10000</a>
%H A263563 Paul Tek, <a href="/A263563/a263563.pl.txt">PERL program for this sequence</a>
%H A263563 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A263563 The following table depicts the first few terms:
%e A263563 +----+--------+-----------------------------------+
%e A263563 | n  | a(n)   | a(n) in situation with leading 0s |
%e A263563 +----+--------+-----------------------------------+
%e A263563 |  1 |      1 | 1                                 |
%e A263563 |  2 |      2 |  2                                |
%e A263563 |  3 |      3 |   3                               |
%e A263563 |  4 |      4 |    4                              |
%e A263563 |  5 |      5 |     5                             |
%e A263563 |  6 |      6 |      6                            |
%e A263563 |  7 |      7 |       7                           |
%e A263563 |  8 |      8 |        8                          |
%e A263563 |  9 |      9 |         9                         |
%e A263563 | 10 |     10 |          10                       |
%e A263563 | 11 |     11 |           011                     |
%e A263563 | 12 |    110 |            110                    |
%e A263563 | 13 |    100 |             100                   |
%e A263563 | 14 |     12 |              0012                 |
%e A263563 | 15 |    120 |               0120                |
%e A263563 | 16 |   1200 |                1200               |
%e A263563 | 17 |     20 |                 200               |
%e A263563 | 18 |     13 |                  0013             |
%e A263563 | 19 |    130 |                   0130            |
%e A263563 | 20 |   1300 |                    1300           |
%e A263563 | 21 |     30 |                     300           |
%e A263563 | 22 |     14 |                      0014         |
%e A263563 | 23 |    140 |                       0140        |
%e A263563 | 24 |   1400 |                        1400       |
%e A263563 | 25 |     40 |                         400       |
%e A263563 | 26 |     15 |                          0015     |
%e A263563 | 27 |    150 |                           0150    |
%e A263563 | 28 |   1500 |                            1500   |
%e A263563 | 29 |     50 |                             500   |
%e A263563 | 30 |     16 |                              0016 |
%e A263563 +----+--------+-----------------------------------+
%e A263563 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 A263563 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 A263563 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 A263563 And so on. (End)
%o A263563 (Perl) See Links section.
%Y A263563 Cf. A263443, A263564.
%K A263563 nonn,base,look,nice
%O A263563 1,2
%A A263563 _Paul Tek_, Oct 21 2015