Tool to generate Conway sequences, a sequence of digits (also called Look-and-Say) where each term is made of the reading of the digits of the previous term.

Conway Sequence - dCode

Tag(s) : Mathematics, Fun/Miscellaneous

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To generate the next term in the sequence, use the previous one, by reading it digit by digit and grouping the numbers that are repeated consecutively. The sequence usually begins with 1 first term (also called seed).

__Example:__

Term | Is read | Is written |
---|---|---|

1 | one 1 | 11 |

11 | two 1s | 21 |

21 | one 2 and one 1 | 1211 |

1211 | one 1, one 2 and two 1s | 111221 |

111221 | three 1s, two 2s and 1 | 312211 |

The **Conway sequence** is 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... (and is often used as a riddle, a logic sequence, where the player must guess the next term)

Conway's sequence is also known as the audioactive suite or *look and say* sequence.

The sequence with seed 1 contains only the digits 1, 2 and 3.

All terms begin with 1 or 3 except the 3rd.

Reductio ad absurdum (assuming the seed does not contain 333):

Suppose that 333 appears for the first time at term n, then the term n-1 must also contain 333 (_333 or 333_ can only appear with a series of three 3 in the previous term). Contradiction, the hypothesis is false, so 333 never appears.

The **Conway sequence** is set to begin with 1 by default, but it is possible to use a different seed.

__Example:__ For a seed g of 2,3,4,5,6,7,8,9 or 0, the sequence obtained is g, 1g, 111g, 311g, 13211g, 111312211g ... (the seed is always at the end).

It is possible to use slightly different rules:

- Read the previous term and count all occurrences of numbers, listed in ascending order.

__Example:__ 1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, ...

- Read the previous term and count all occurrences of numbers, listed in descending order.

__Example:__ 1, 11, 21, 1211, 1231, 131221, 132231, 232221, 134211, 14131231, 14231241, ...

- Read the previous term and count all occurrences of numbers, listed in order of appearance.

__Example:__ 1, 11, 21, 1211, 3112, 132112, 311322, 232122, 421311, 14123113 ...

The **Conway sequence** is similar to run-length encoding.

This sequence has been invented and analyzed by famous mathematician John H. Conway.

`// Yves PRATTER`

// Version 1.0 - 2011/11/07

function previousConway(t) {

r = "";

if (t.length%2 == 1) return r;// impossible

idx = 0;

while (idx < t.length){

for(i=0; i < t.charAt(idx); i++) { r += t.charAt(idx+1); }

idx += 2;

}

return r;

}

function conway(t) {

if (t == "") return "0";

r = "";

idx = 0;

while (idx < t.length){

for(i=1; t.charAt(idx+i) == t.charAt(idx); i++) {}

r += i + t.charAt(idx);

idx += i;

}

return r;

}

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NB: for encrypted messages, test our automatic cipher identifier!

sequence,conway,look,say,audioactive,11,21,1211,111221,312211,13112221,1113213211

Source : https://www.dcode.fr/conway-sequence

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