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 1-5 of 5 results.

A303783 Lexicographically earliest sequence of distinct terms such that what emerges from the mask is a square (see the Comment section for the mask explanation).

Original entry on oeis.org

1, 10, 2, 11, 3, 14, 4, 19, 5, 20, 6, 21, 7, 24, 8, 29, 9, 30, 100, 12, 101, 13, 104, 15, 109, 16, 110, 17, 111, 18, 114, 22, 119, 23, 120, 25, 121, 26, 124, 27, 129, 28, 130, 31, 131, 32, 134, 33, 139, 34, 140, 35, 141, 36, 144, 37, 149, 38, 150, 39, 151, 40, 154, 41, 159, 42, 160, 43, 161, 44, 164, 45, 169, 46, 170, 47
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Apr 30 2018

Keywords

Comments

For any pair of contiguous terms, one of the terms uses fewer digits than the other. This term is called the mask. Put the mask on the other term, starting from the left. What is not covered by the mask forms a square number.
The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
This sequence is a permutation of the integers > 0, as all integers will appear at some point, either as mask or masked.

Examples

			In the pair (1,10), 1 is the mask; 0 emerges and is a square;
in the pair (10,2), 2 is the mask; 0 emerges and is a square;
in the pair (2,11), 2 is the mask; 1 emerges and is a square;
in the pair (11,3), 3 is the mask; 1 emerges and is a square;
...
in the pair (11529,2018), 2018 is the mask; 9 emerges and is a square;
etc.

Links

Crossrefs

Cf. A303782 (same idea with primes), A303784 (with even numbers), A303785 (with odd numbers), A303786 (rebuilds the sequence itself term by term).

A303784 Lexicographically earliest sequence of distinct terms such that what emerges from the mask is even (see the Comment section for the mask explanation).

Original entry on oeis.org

1, 10, 2, 12, 3, 14, 4, 16, 5, 18, 6, 20, 7, 22, 8, 24, 9, 26, 100, 11, 102, 13, 104, 15, 106, 17, 108, 19, 110, 21, 112, 23, 114, 25, 116, 27, 118, 28, 120, 29, 122, 30, 124, 31, 126, 32, 128, 33, 130, 34, 132, 35, 134, 36, 136, 37, 138, 38, 140, 39, 142, 40, 144, 41, 146, 42, 148, 43, 150, 44, 152, 45, 154, 46, 156, 47
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Apr 30 2018

Keywords

Comments

For any pair of contiguous terms, one of the terms uses fewer digits than the other. This term is called the mask. Put the mask on the other term, starting from the left. What is not covered by the mask forms an even number.
The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
This sequence is a permutation of the integers > 0, as all integers will appear at some point, either as mask or masked.

Examples

			In the pair (1,10), 1 is the mask; 0 emerges and is even;
In the pair (10,2), 2 is the mask; 0 emerges and is even;
In the pair (2,12), 2 is the mask; 2 emerges and is even;
In the pair (12,3), 3 is the mask; 2 emerges and is even;
...
In the pair (690,2018), 690 is the mask; 8 emerges and is even;
etc.

Links

Crossrefs

Cf. A303782 (same idea with primes), A303783 (with squares), A303785 (with odd numbers), A303786 (rebuilds term by term the sequence itself).

A303785 Lexicographically earliest sequence of distinct terms such that what emerges from the mask is odd (see the Comment section for the mask explanation).

Original entry on oeis.org

1, 11, 2, 13, 3, 15, 4, 17, 5, 19, 6, 21, 7, 23, 8, 25, 9, 27, 101, 10, 103, 12, 105, 14, 107, 16, 109, 18, 111, 20, 113, 22, 115, 24, 117, 26, 119, 28, 121, 29, 123, 30, 125, 31, 127, 32, 129, 33, 131, 34, 133, 35, 135, 36, 137, 37, 139, 38, 141, 39, 143, 40, 145, 41, 147, 42, 149, 43, 151, 44, 153, 45, 155, 46, 157, 47
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Apr 30 2018

Keywords

Comments

For any pair of contiguous terms, one of the terms uses fewer digits than the other. This term is called the mask. Put the mask on the other term, starting from the left. What is not covered by the mask forms an odd number.
The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
This sequence is a permutation of the integers > 0, as all integers will appear at some point, either as mask or masked.

Examples

			In the pair (1,11), 1 is the mask; 1 emerges and is odd;
In the pair (11,2), 2 is the mask; 1 emerges and is odd;
In the pair (2,13), 2 is the mask; 3 emerges and is odd;
In the pair (13,3), 3 is the mask; 3 emerges and is odd;
...
In the pair (11019,2018), 2018 is the mask; 9 emerges and is odd;
etc.

Links

Crossrefs

Cf. A303782 (same idea with primes), A303783 (with squares), A303784 (with even numbers), A303786 (rebuilds the sequence itself term by term).

A303786 Lexicographically earliest sequence of distinct terms such that what emerges from the mask rebuilds the sequence itself, term by term (see the Comment section for the mask explanation).

Original entry on oeis.org

1, 11, 1011, 10001011, 1000000010001011, 10000000000000001000000010001011, 1000000000000000000000000000000010000000000000001000000010001011, 10000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000010000000000000001000000010001011
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, Apr 30 2018

Keywords

Comments

For any pair of contiguous terms, one of the terms uses fewer digits than the other. This term is called the mask. Put the mask on the other term, starting from the left. What is not covered by the mask rebuilds, term by term, the starting sequence.
The n-th term of the sequence has exactly 2^(n-1) digits, which means that a(21) has more than one million digits.
The sequence starts with a(1) = 1, then a(n) = 10^(2^(n-1)-1)+a(n-1).

Examples

			In the pair (1,11), 1 is the mask; 1 emerges = a(1);
In the pair (11,1011), 11 is the mask; 11 emerges = a(2);
In the pair (1011,10001011), 1011 is the mask; 1011 emerges = a(3); etc.

Links

Crossrefs

Cf. A303782 (same idea with primes), A303783 (with squares), A303784 (with even numbers), A303785 (with odd numbers).

A303847 Lexicographically earliest sequence of distinct terms such that what emerges from the mask (right-aligned) is prime (see the Comments section for the mask explanation).

Original entry on oeis.org

1, 20, 2, 21, 3, 22, 4, 23, 5, 24, 6, 25, 7, 26, 8, 27, 9, 28, 200, 10, 201, 11, 202, 12, 203, 13, 204, 14, 205, 15, 206, 16, 207, 17, 208, 18, 209, 19, 210, 29, 211, 30, 212, 31, 213, 32, 214, 33, 215, 34, 216, 35, 217, 36, 218, 37, 219, 38, 220, 39, 221, 40, 222, 41, 223, 42, 224, 43, 225, 44, 226, 45, 227, 46, 228, 47
Offset: 1

Views

Author

Eric Angelini and Jean-Marc Falcoz, May 01 2018

Keywords

Comments

For any pair of consecutive terms, one of the terms uses fewer digits than the other. This term is called the mask. Put the mask on the other term, starting from the right. What is not covered by the mask forms a prime number on the left.
The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
This sequence is a permutation of the positive integers, as all integers will appear at some point, either as mask or masked.

Examples

			In the pair (1,20), 1 is the mask; 2 emerges and is prime;
in the pair (20,2), 2 is the mask; 2 emerges and is prime;
in the pair (2,21), 2 is the mask; 2 emerges and is prime;
in the pair (21,3), 3 is the mask; 2 emerges and is prime;
...
in the pair (117,2018), 117 is the mask; 2 emerges and is prime;
etc.

Links

Crossrefs

Cf. A303782 (same idea, but the mask is left-aligned).
Showing 1-5 of 5 results.

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

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