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Conmethod Sequence Generator

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How does the Conmeans Sequence works?

To geneprice the next term in the sequence, usage the previous one, by reading it digit by digit and grouping the numbers that are repetitive consecutively. The sequence typically begins through 1 initially term (also dubbed seed).

You are watching: 1 then 11 then 21 then 1211

 1 one 1 11 11 two 1s 21 21 one 2 and also one 1 1211 1211 one 1, one 2 and 2 1s 111221 111221 3 1s, 2 2s and 1 312211

The Conmethod sequence is 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ... (and also is regularly supplied as a riddle, a logic sequence, where the player have to guess the following term)

Conway"s sequence is also well-known as the audioenergetic suite or look and also say sequence.

The sequence via seed 1 includes only the digits 1, 2 and also 3.

All terms start through 1 or 3 except the 3rd.

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Can the sequence contain "333"?

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

Suppose that 333 shows up for the initially time at term n, then the term n-1 need to also contain 333 (_333 or 333_ have the right to only show up via a series of 3 3 in the previous term). Contradiction, the hypothesis is false, so 333 never appears.

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What are the variants of the Conmeans Sequence?

The Conmeans sequence is collection to start via 1 by default, however it is feasible to use a various seed.

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

It is feasible to usage slightly different rules:

- Read the previous term and also 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 also count all cases of numbers, noted in descfinishing order.

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

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

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

The Conmethod sequence is similar to run-length encoding.

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Why is the sequence dubbed the Conway Sequence?

This sequence has been developed and analyzed by famed mathematician John H. Conway.

See more: Alliteration And Onomatopoeia Poems, Alliteration And Onomatopoeia

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Source code

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sequence,conmeans,look,say,audioenergetic,11,21,1211,111221,312211,13112221,1113213211