A210423 -id:A210423 - cp's OEIS frontend

A098670 Start with a(1) = 5. Construct slowest growing sequence such that the statement "the a(n)-th digit is a 2" is true for all n.

5, 6, 7, 8, 22, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270

Offset: 1

Eric Angelini, Oct 27 2004

The sequence goes 5, 6, 7, 8, 22, 220, 221, ..., 290, 2222, 22222, 222222, ... for 275 more digits, then for most of the rest of the sequence, a(n+1)=a(n)+1. Starting with a(1)=3 yields 3, 4, 22, 23, ..., 30, 32, 222, 2222, 2223,... for at least 2000 more digits. (The 222nd digit happens to be the initial digit of a(63)=2271.) Starting with a(1)=4 yields 4, 5, 6, 22, 23, ..., 30, 222, 2222, 2223, ... See A210416 for a variant without requirement of growth. - M. F. Hasler, Oct 08 2013

			The 5th digit of the sequence is a "2", the 6th digit also, then the 7th, the 8th, the 22nd etc.

Index to the OEIS: Entries related to self-referencing sequences.

Cf. A114134, A098645, A210414-A210423.

{ a=5; P=Set(); L=0; while(1, print1(a,", "); P=setunion(P,Set([a])); L+=#Str(a); until(g, g=1; a++; s=Vec(Str(a)); for(i=1,#s, if(setsearch(P,L+i)&&s[i]!="2",g=0;break)); ); ) } \\ Max Alekseyev

Edited and extended by Max Alekseyev, Feb 06 2010

A114134 Start with a(1) = 1. For n>1, choose a(n) to be the smallest number > a(n-1) consistent with the condition that "the a(n)-th digit is a 1" is true for all n.

Original entry on oeis.org

1, 3, 10, 11, 12, 21, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 1111, 11111, 111111, 1111111, 11111111, 11111112, 11111113

Offset: 1

Eric Angelini, Oct 27 2004

There can be 1's in other positions too.

Sequence A098645 does not allow 1's in other positions, A210415 is a variant which does not impose a(n)>a(n-1). - M. F. Hasler, Oct 08 2013

			The first digit of the sequence is a "1", the 3rd digit also, then the 10th, the 11th, etc.

Index to the OEIS: Entries related to self-referencing sequences.

Cf. A098670. See A098645 for another version.

Cf. A210414-A210423.

Entry revised by Eric Angelini and N. J. A. Sloane, Feb 03 2006.

More terms from Rick L. Shepherd, Feb 05 2006

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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cp's OEIS Frontend

A098670 Start with a(1) = 5. Construct slowest growing sequence such that the statement "the a(n)-th digit is a 2" is true for all n.

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A114134 Start with a(1) = 1. For n>1, choose a(n) to be the smallest number > a(n-1) consistent with the condition that "the a(n)-th digit is a 1" is true for all n.

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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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Perl