A263443 A self-describing sequence: when the sequence is read as a string of decimal digits, a(n) gives the starting position of an occurrence of n. This sequence is the lexicographically earliest one with this property.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 14, 1, 17, 130, 21, 50, 15, 28, 180, 33, 20, 37, 2, 200, 42, 52, 47, 270, 162, 60, 57, 310, 300, 3, 66, 350, 35, 73, 380, 78, 400, 41, 84, 302, 4, 91, 460, 96, 480, 22, 104, 510, 110, 530, 115, 5, 55, 122, 580, 53, 132, 146, 136

Offset: 1

Author

Paul Tek, Oct 18 2015

Keywords

• nonn
• base

Comments

The sequence does not necessarily give the earliest position of a number.

For example, 1234 first appears at position 1, but a(1234) = 28011.

Examples

			The following table lists few first terms, with the corresponding digits induced in the overall sequence:
+----+------+------------------------------------------------------------+
| n  | a(n) | New known digits                                           |
+----+------+------------------------------------------------------------+
|  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 |   14 |            1411                                            |
| 12 |    1 |                                                            |
| 13 |   17 |                713                                         |
| 14 |  130 |                   0                                 ... 14 |
| 15 |   21 |                    215                                     |
| 16 |   50 |                       0                          16        |
| 17 |   15 |                        15                                  |
| 18 |   28 |                          2818                              |
+----+------+------------------------------------------------------------+
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000
• Paul Tek, PERL program for this sequence

Crossrefs

Cf. A048991, A114315, A125132, A210423.

Programs

Perl

See Links section.