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

1,2

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.

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

Example

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)

Prog

(Perl) See Links section.

Crossrefs

Cf. A263443, A263564.

Sequence in context: A068634 A049872 A239218 * A004873 A043316 A044913

Adjacent sequences: A263560 A263561 A263562 * A263564 A263565 A263566

Keyword

nonn,base,look,nice

Author

Paul Tek, Oct 21 2015

Status

approved