A125132 -id:A125132 - cp's OEIS frontend

A125133 Numbers missing from A125132.

4, 6, 18, 20, 22, 24, 26, 38, 40, 42, 44, 46, 58, 60, 62, 64, 66, 78, 80, 82, 84, 86, 100, 102, 104, 106, 108, 112, 113, 115, 117, 119, 121, 122, 123, 125, 127, 129, 131, 132, 133, 135, 137, 139, 141, 142, 143, 145, 147, 149, 151, 153, 155, 158, 161, 164, 167

Offset: 1

N. J. A. Sloane, Jan 12 2007

Digit positions in A125132-with-digits-strung-together where even digits appear.

			4 and 6 are members because the 4th and 6th digits in that string are even (2 and 8 respectively).

More terms from D. S. McNeil, Oct 22 2011

A114308 Self-describing sequence: sequence starts with a(1) = 1 and a(n) is chosen to be the smallest number > a(n-1) such that the assertion "sequence gives the positions of the odd digits when the sequence is read as a string of digits" is true.

Original entry on oeis.org

1, 4, 6, 7, 8, 9, 11, 12, 13, 16, 21, 22, 24, 31, 41, 42, 44, 46, 50, 60, 62, 64, 66, 71, 81, 83, 84, 85, 86, 88, 200, 201, 210, 301, 400, 410, 420, 422, 423, 431, 510, 520, 600, 602, 604, 606, 608, 620, 622, 624, 626, 628, 640, 642, 644, 646, 648, 660

Offset: 1

Eric Angelini, Feb 05 2006

			Brackets indicate the odd digits in the sequence:
Sequence: (1),4,6,(7),8,(9),(1)(1),(1)2, (1)(3),(1)6
Positions of odd digits: 1st 4th 6th 7th 8th 9th 11th 12th 13th ..., which is the sequence itself.

N. J. A. Sloane, Table of n, a(n) for n = 1..480

Cf. A125132.

More terms from N. J. A. Sloane, Jan 10 2007

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.

Original entry on oeis.org

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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See Links section.
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A297121 Self-describing sequence: sequence starts with a(1) = 2 and a(n) is chosen to be the smallest positive number not already in the sequence such that the assertion "sequence gives the positions of the even digits when the sequence is read as a string of digits" is true.

Original entry on oeis.org

2, 4, 1, 6, 7, 8, 20, 10, 12, 14, 16, 18, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 21, 19, 23, 25, 37, 39, 41, 43, 45, 57, 59, 61, 63, 65, 77, 79, 81, 83, 85, 99, 104, 106, 112

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Dec 26 2017

Inspired by Sloane's sequence A125132.

			Here are the digits strung together (the even digits occur at positions that are indexed by terms of the sequence):
-241678201
0121416182
2242628303
2343638404...
Explanation: a(2) must be even, so a(2)=4; a(3)=1; a(4) must be even, so a(4)=6; a(5) cannot be 3 or 5 (contradiction) thus a(5)=7. And so on.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..2001

A342164 A self-describing sequence: start with 0, then for each digit in each successive term, starting from the first term, append to the sequence its most recent position in the string formed by the concatenation of all previous terms.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 17, 19, 16, 23, 18, 27, 30, 27, 22, 27, 24, 39, 41, 44, 28, 47, 50, 41, 52, 56, 50, 56, 56, 56, 50, 56, 53, 72, 42, 75, 54, 80, 80, 76, 83, 80, 85, 92, 90, 80, 54, 99, 94, 99, 86, 99, 98, 99, 108, 99, 108, 99, 108, 99, 126, 99

Offset: 0

Scott R. Shannon, Mar 03 2021

After the leading zero taking the a(n)-th digit of the sequence returns the digits of the sequence.

			The second term is 1 as the 0 in the first term appears as the first digit in the sequence. Likewise the third term is 2 as the 1 in the second term is the second digit of the sequence, and so on to the eleventh term.
As the eleventh term is 10 and has two digits, the twelfth and thirteenth terms give the most recent position of a 1 and 0 in the sequence, and they appear at the eleventh and twelfth position.
As the twelfth term is 11, the fourteenth and fifteenth terms give the most recent position of the two 1's. The last 1 appears at the fifteenth position, and after appending 15, which contains a 1, the most recent 1 now appears at the seventeenth position.

Cf. A125132, A264646, A114308, A263563, A308387

cp's OEIS Frontend

A125133 Numbers missing from A125132.

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A114308 Self-describing sequence: sequence starts with a(1) = 1 and a(n) is chosen to be the smallest number > a(n-1) such that the assertion "sequence gives the positions of the odd digits when the sequence is read as a string of digits" is true.

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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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Perl

A297121 Self-describing sequence: sequence starts with a(1) = 2 and a(n) is chosen to be the smallest positive number not already in the sequence such that the assertion "sequence gives the positions of the even digits when the sequence is read as a string of digits" is true.

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A342164 A self-describing sequence: start with 0, then for each digit in each successive term, starting from the first term, append to the sequence its most recent position in the string formed by the concatenation of all previous terms.

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