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 1-4 of 4 results.

A351996 A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only prime numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.

Original entry on oeis.org

1, 10, 101, 103, 107, 109, 111, 11, 12, 2, 3, 4, 13, 14, 17, 15, 5, 6, 21, 7, 8, 19, 16, 27, 9, 18, 23, 29, 33, 20, 113, 30, 117, 31, 22, 39, 24, 37, 25, 43, 41, 47, 51, 49, 53, 59, 63, 57, 69, 61, 67, 71, 32, 73, 34, 77, 35, 79, 36, 81, 83, 89, 93, 26, 87, 99, 28, 121, 38, 123, 40, 119, 42, 127, 44, 91, 50
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Feb 27 2022

Keywords

Comments

The sequence is a permutation of the positive integers.

Examples

			1 is expelled from a(1) = 1 and hits the 0 of a(2) = 10, turning this integer into 11, a prime;
0 is expelled from a(2) = 10 and hits the 0 of a(3) = 101, leaving this prime unchanged;
0 is expelled from a(3) = 101 and hits the 0 of a(4) = 103, leaving this prime unchanged;
0 is expelled from a(4) = 103 and hits the 0 of a(5) = 107, leaving this prime unchanged;
0 is expelled from a(5) = 107 and hits the 0 of a(6) = 109, leaving this prime unchanged;
0 is expelled from a(6) = 109 and hits the middle 1 of a(7) = 111, turning this integer into 101, a prime;
1 is expelled from a(7) = 111 and hits one 1 of a(8) = 11, leaving this prime unchanged;
1 is expelled from a(8) = 11 and hits the 2 of a(9) = 12, turning this integer into 11, a prime;
2 is expelled from a(9) = 12 and hits the 2 of a(10) = 2, leaving this prime unchanged; etc.
From _Jon E. Schoenfield_, Mar 01 2022: (Start)
The chain reaction is depicted in the chart below:
.
  | Step | Step | Step | Step | Step | Step | Step | Step | Step | Step |
  |   1  |   2  |   3  |   4  |   5  |   6  |   7  |   8  |   9  |  10  |
  |      |      |      |      |      |      |      |      |      |      |
  |   :  |      |      |      |      |      |      |      |      |      |
  |   1  |      |      |      |      |      |      |      |      |      |
  |  10  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |
  |      |   0  |      |      |      |      |      |      |      |      |
  |  101 |  101 |  101 |  101 |  101 |  101 |  101 |  101 |  101 |  101 |
  |      |      |   0  |      |      |      |      |      |      |      |
  |  103 |  103 |  103 |  103 |  103 |  103 |  103 |  103 |  103 |  103 |
  |      |      |      |   0  |      |      |      |      |      |      |
  |  107 |  107 |  107 |  107 |  107 |  107 |  107 |  107 |  107 |  107 |
  |      |      |      |      |   0  |      |      |      |      |      |
  |  109 |  109 |  109 |  109 |  109 |  109 |  109 |  109 |  109 |  109 |
  |      |      |      |      |      |   0  |      |      |      |      |
  |  111 |  111 |  111 |  111 |  111 |  111 |  101 |  101 |  101 |  101 |
  |      |      |      |      |      |      |   1  |      |      |      |
  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |  11  |
  |      |      |      |      |      |      |      |   1  |      |      |
  |  12  |  12  |  12  |  12  |  12  |  12  |  12  |  12  |  11  |  11  |
  |      |      |      |      |      |      |      |      |   2  |      |
  |   2  |   2  |   2  |   2  |   2  |   2  |   2  |   2  |   2  |   2  |
(End)

Links

Crossrefs

Cf. A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).

A352000 A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only square numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.

Original entry on oeis.org

1, 2, 15, 3, 16, 4, 5, 20, 100, 101, 6, 10, 102, 25, 35, 26, 45, 7, 129, 8, 11, 9, 40, 103, 36, 46, 19, 56, 21, 66, 12, 55, 22, 65, 13, 76, 184, 80, 104, 29, 75, 229, 85, 31, 86, 41, 39, 96, 42, 95, 43, 124, 81, 82, 111, 83, 161, 84, 49, 59, 23, 224, 121, 125, 87, 284, 131, 261, 141, 60, 105, 24, 61, 88
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Feb 27 2022

Keywords

Comments

The sequence is a permutation of the integers > 0.

Examples

			1 is expelled from a(1) = 1 and hits the 2 of a(2) = 2, turning this integer into 1, a square number;
2 is expelled from a(2) = 2 and hits the 1 of a(3) = 15, turning this integer into 25, a square number;
1 is expelled from a(3) = 15 and hits the 3 of a(4) = 3, turning this integer into 1, a square number;
3 is expelled from a(4) = 3 and hits the 1 of a(5) = 16, turning this integer into 36, a square number;
1 is expelled from a(5) = 16 and hits the 4 of a(6) = 4, turning this integer into 1, a square number;
4 is expelled from a(6) = 4 and hits the 5 of a(7) = 5, turning this integer into 4, a square number;
5 is expelled from a(7) = 5 and hits the 0 of a(8) = 20, turning this integer into 25, a square number;
0 is expelled from a(8) = 20 and hits a 0 of a(9) = 100, "turning" this integer into 100, a square number;
0 is expelled from a(9) = 100 and hits the rightmost 1 of a(10) = 101, turning this integer into 100, a square number; etc.

Links

Crossrefs

Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351998 (even numbers left), A351999 (Fibonacci numbers left), A000290 (the squares).

A351998 A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only even numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.

Original entry on oeis.org

1, 10, 12, 14, 16, 18, 20, 2, 3, 22, 4, 5, 24, 6, 7, 26, 8, 9, 28, 11, 30, 32, 34, 36, 38, 40, 13, 42, 15, 44, 17, 46, 19, 48, 21, 50, 52, 54, 56, 58, 60, 23, 62, 25, 64, 27, 66, 29, 68, 31, 70, 72, 74, 76, 78, 80, 33, 82, 35, 84, 37, 86, 39, 88, 41, 90, 92, 94, 96, 98, 100, 43, 102, 45, 104, 47, 106, 49
Offset: 1

Views

Author

Eric Angelini ansd Carole Dubois, Feb 27 2022

Keywords

Comments

The sequence is a permutation of the integers > 0.

Examples

			1 is expelled from a(1) = 1 and hits the 1 of a(2) = 10, "turning" this integer into 10, an even number;
1 is expelled from a(2) = 10 and hits the 1 of a(3) = 12, "turning" this integer into 12, an even number;
1 is expelled from a(3) = 12 and hits the 1 of a(4) = 14, "turning" this integer into 14, an even number;
1 is expelled from a(4) = 14 and hits the 1 of a(5) = 16, "turning" this integer into 16, an even number;
1 is expelled from a(5) = 16 and hits the 1 of a(6) = 18, "turning" this integer into 18, an even number;
1 is expelled from a(6) = 18 and hits the 2 of a(7) = 20, turning this integer into 10, an even number;
2 is expelled from a(7) = 20 and hits the 2 of a(8) = 2, "turning" this integer into 2, an even number;
2 is expelled from a(8) = 2 and hits the 3 of a(9) = 3, turning this integer into 2, an even number;
3 is expelled from a(9) = 3 and hits the leftmost 2 of a(10) = 22, turning this integer into 32, an even number; etc.

Links

Crossrefs

Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351999 (Fibonacci numbers left), A352000 (square numbers left).

A351999 A chain reaction sequence: a digit d1 from a(n) is expelled towards a(n+1) where it hits a digit d2 [from a(n+1)] and replaces it; d2 in turn is expelled towards a(n+2), hits a digit d3 there and replaces it; d3 in turn is expelled towards a(n+3), hits a digit there, and replaces it; d4 is expelled... etc. At the end of the chain reaction, only Fibonacci numbers will be left. This is the lexicographically earliest sequence of distinct positive integers with this property.

Original entry on oeis.org

1, 2, 3, 4, 30, 610, 611, 5, 6, 110, 7, 307, 612, 8, 9, 80, 613, 10, 614, 31, 13, 20, 615, 15, 21, 22, 11, 23, 12, 41, 32, 51, 25, 61, 210, 71, 317, 24, 33, 14, 26, 310, 16, 410, 34, 35, 45, 36, 510, 50, 616, 710, 327, 81, 19, 27, 337, 17, 347, 37, 357, 52, 91, 82, 133, 28, 29, 233, 333, 18, 39, 44
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Feb 27 2022

Keywords

Comments

The sequence is a permutation of the integers > 0.

Examples

			1 is expelled from a(1) = 1 and hits the 2 of a(2) = 2, "turning" this integer into 2, a Fibonacci number;
2 is expelled from a(2) = 2 and hits the 3 of a(3) = 3, "turning" this integer into 3, a Fibonacci number;
3 is expelled from a(3) = 3 and hits the 4 of a(4) = 4, turning this integer into 3, a Fibonacci number;
4 is expelled from a(4) = 4 and hits the 0 of a(5) = 30, turning this integer into 34, a Fibonacci number;
0 is expelled from a(5) = 30 and hits the 0 of a(6) = 610, "turning" this integer into 610, a Fibonacci number;
0 is expelled from a(6) = 610 and hits the rightmost 1 of a(7) = 611, turning this integer into 610, a Fibonacci number;
1 is expelled from a(7) = 611 and hits the 5 of a(8) = 5, turning this integer into 1, a Fibonacci number;
5 is expelled from a(8) = 5 and hits the 6 of a(9) = 6, turning this integer into 5, a Fibonacci number;
6 is expelled from a(9) = 110 and hits the leftmost 1 of a(7) = 110, turning this integer into 610, a Fibonacci number; etc.

Links

Crossrefs

Cf. A351996 (prime numbers left), A351997 (odd numbers left), A351998 (even numbers left), A352000 (square numbers left), A000045 (Fibonacci numbers).
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.