A114315 -id:A114315 - cp's OEIS frontend

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

Paul Tek, Oct 18 2015

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

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

			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                              |
+----+------+------------------------------------------------------------+

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

Cf. A048991, A114315, A125132, A210423.

Perl
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A203620 A self-describing sequence: when the sequence is read as a string of digits, a(n) says the position of the digits that are prime.

Original entry on oeis.org

2, 3, 5, 1, 7, 8, 22, 11, 20, 15, 21, 14, 23, 25, 26, 27, 29, 31, 32, 19, 35, 36, 37, 39, 40, 41, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 90, 92, 94, 98, 105, 109, 200, 115, 201, 114, 122, 123, 125, 126

Offset: 1

Paolo P. Lava, Feb 15 2012

Digits in position a(n) are prime, namely 2, 3, 5 or 7. Any step chooses the minimum integer not yet present in the sequence and not leading to a contradiction.

			The sequence cannot start with 1 because the first digit, 1 itself, is not prime. Then let us put 2. The next digit must be prime: 3. Even the third must be prime: 5. No specific indications for the fourth digit. We can choose 1 because the first digit, 2, is prime. The fifth must be prime: 7. And so on.

Index to sequences related to say what you see

Cf. A114315 and A121053.

cp's OEIS Frontend

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.

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