cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A342077 Prime digits only come in successive pairs (separated or not by a comma).

Original entry on oeis.org

1, 2, 20, 3, 30, 4, 5, 50, 6, 7, 70, 8, 9, 10, 11, 12, 21, 13, 31, 14, 15, 51, 16, 17, 71, 18, 19, 22, 33, 40, 41, 42, 23, 32, 24, 43, 34, 44, 45, 52, 25, 53, 35, 54, 46, 47, 72, 26, 48, 49, 55, 60, 61, 62, 27, 73, 36, 63, 37, 74, 64, 65, 56, 66, 67, 75, 57, 76, 68, 69, 77, 80, 81, 82, 28, 83, 38
Offset: 1

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Author

Eric Angelini, Feb 28 2021

Keywords

Comments

The sequence starts with a(1) = 1 and is always extended with the smallest positive integer not yet present that does not lead to a contradiction.

Examples

			a(2) = 2 forces the next digit to be a 2 (as prime digits must come in pairs); the smallest positive integer not yet present that starts with a 2 is 20. Thus, a(3) = 20;
a(4) = 3 as 3 is the smallest positive integer not yet present that does not lead to a contradiction;
a(5) = 30 as 30 is the smallest positive integer not yet present that does not lead to a contradiction and starts with a 3; etc.

Crossrefs

Cf. A342076, A342078 and A342079 (variations on the same idea)

Programs

A342078 Odd digits only come in successive pairs (separated or not by a comma).

Original entry on oeis.org

1, 10, 2, 3, 30, 4, 5, 50, 6, 7, 70, 8, 9, 90, 11, 20, 21, 12, 22, 23, 31, 13, 32, 24, 25, 51, 14, 26, 27, 71, 15, 52, 28, 29, 91, 16, 33, 40, 41, 17, 72, 42, 43, 34, 44, 45, 53, 35, 54, 46, 47, 73, 36, 48, 49, 92, 55, 60, 61, 18, 62, 63, 37, 74, 64, 65, 56, 66, 67, 75, 57, 76, 68
Offset: 1

Views

Author

Eric Angelini, Feb 28 2021

Keywords

Comments

The sequence starts with a(1) = 1 and is always extended with the smallest positive integer not yet present that does not lead to a contradiction.

Examples

			a(1) = 1 forces the next digit to be a 1 (as odd digits must come in pairs); the smallest positive integer not yet present that starts with a 1 and does not lead to a contradiction is 10. Thus, a(2) = 10;
a(3) = 2 as the smallest positive integer not yet present that does not lead to a contradiction is 2;
a(4) = 3 as the smallest positive integer not yet present that does not lead to a contradiction is 3;
a(5) = 30 as a(5) must start with a 3 (the odd digits must come in pairs) and 30 is the smallest positive integer not yet present that does not lead to a contradiction; etc.

Crossrefs

Cf. A342076, A342077 and A342079 (variations on the same idea).

Programs

A342079 Even digits only come in successive pairs (separated or not by a comma).

Original entry on oeis.org

1, 2, 21, 3, 4, 41, 5, 6, 61, 7, 8, 81, 9, 11, 12, 22, 23, 13, 14, 42, 24, 43, 15, 16, 62, 25, 17, 18, 82, 26, 63, 19, 31, 32, 27, 33, 34, 44, 45, 35, 36, 64, 46, 65, 37, 38, 83, 39, 51, 52, 28, 84, 47, 53, 54, 48, 85, 55, 56, 66, 67, 57, 58, 86, 68, 87, 59, 71, 72, 29, 73, 74, 49, 75, 76, 69, 77, 78, 88, 89
Offset: 1

Views

Author

Eric Angelini, Feb 28 2021

Keywords

Comments

The sequence starts with a(1) = 1 and is always extended with the smallest positive integer not yet present that does not lead to a contradiction.
No term can end with an odd number of successive 0.

Examples

			a(2) = 2 as the smallest positive integer not yet present that does not lead to a contradiction is 2;
a(3) = 21 (and not 20, as no term can end with an odd number of successive 0), because 21 is the smallest positive integer not yet present that completes a pair of identical even digits (2-2) and that does not lead to a contradiction;
a(4) = 3 as the smallest positive integer not yet present that does not lead to a contradiction is 3;
a(5) = 4 as the smallest positive integer not yet present that does not lead to a contradiction is 4;
a(6) = 41 (and not 40, as no term can end with an odd number of successive 0), because 41 is the smallest positive integer not yet present that completes a pair of identical even digits (4-4) and that does not lead to a contradiction; etc.

Crossrefs

Cf. A342076, A342077 and A342078 (variations on the same idea).

Programs

Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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