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.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 110, 100, 12, 120, 1200, 20, 13, 130, 1300, 30, 14, 140, 1400, 40, 15, 150, 1500, 50, 16, 160, 1600, 60, 17, 170, 1700, 70, 18, 180, 1800, 80, 19, 190, 1900, 90, 21, 210, 2100, 1000, 22, 220, 2200, 22000, 200, 23, 230, 2300

Offset: 1

Author

Paul Tek, Oct 21 2015

Keywords

• nonn
• base
• look
• nice

Comments

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

The table in the Example section makes the definition clearer.

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

Examples

			The following table depicts the first few terms:
+----+--------+-----------------------------------+
| n  | a(n)   | a(n) in situation with leading 0s |
+----+--------+-----------------------------------+
|  1 |      1 | 1                                 |
|  2 |      2 |  2                                |
|  3 |      3 |   3                               |
|  4 |      4 |    4                              |
|  5 |      5 |     5                             |
|  6 |      6 |      6                            |
|  7 |      7 |       7                           |
|  8 |      8 |        8                          |
|  9 |      9 |         9                         |
| 10 |     10 |          10                       |
| 11 |     11 |           011                     |
| 12 |    110 |            110                    |
| 13 |    100 |             100                   |
| 14 |     12 |              0012                 |
| 15 |    120 |               0120                |
| 16 |   1200 |                1200               |
| 17 |     20 |                 200               |
| 18 |     13 |                  0013             |
| 19 |    130 |                   0130            |
| 20 |   1300 |                    1300           |
| 21 |     30 |                     300           |
| 22 |     14 |                      0014         |
| 23 |    140 |                       0140        |
| 24 |   1400 |                        1400       |
| 25 |     40 |                         400       |
| 26 |     15 |                          0015     |
| 27 |    150 |                           0150    |
| 28 |   1500 |                            1500   |
| 29 |     50 |                             500   |
| 30 |     16 |                              0016 |
+----+--------+-----------------------------------+
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.
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.
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.
And so on. (End)
		

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

Crossrefs

Cf. A263443, A263564.

Programs

Perl

See Links section.