Next Look-and-Say hatchet GeneratorTerm/Number
|Calcul||next Term previous Term|
Conway succession GeneratorInitial ax (seed) Generate
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How walk the Conway sequence works?
To generate the next term in the sequence, use the ahead one, by reading it number by digit and also grouping the numbers that are recurring consecutively. The succession usually starts with 1 first term (also called seed).
You are watching: 1 11 21 1211 111221 312211
|21||one 2 and one 1||1211|
|1211||one 1, one 2 and also 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 frequently used as a riddle, a logic sequence, where the player need to guess the following term)
Conway"s succession is also known as the audioactive suite or look and also say sequence.
The sequence v seed 1 includes only the number 1, 2 and also 3.
All terms start with 1 or 3 except the 3rd.
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Can the sequence contain "333"?
Reductio advertisement absurdum (assuming the seed does not contain 333):
Suppose that 333 shows up for the very first time in ~ term n, climate the hatchet n-1 must additionally contain 333 (_333 or 333_ deserve to only show up with a collection of three 3 in the vault term). Contradiction, the theory is false, therefore 333 never ever appears.
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What space the variants the the Conway Sequence?
The Conway sequence is set to start with 1 by default, yet it is feasible to usage a different seed.
Example: because that a seeds g of 2,3,4,5,6,7,8,9 or 0, the sequence acquired is g, 1g, 111g, 311g, 13211g, 111312211g ... (the particle is constantly at the end).
It is possible to usage slightly different rules:
- review the previous term and also count all cases of numbers, listed in ascending order.
Example: 1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, ...
- check out the vault term and also count all incidents of numbers, provided in descending order.
Example: 1, 11, 21, 1211, 1231, 131221, 132231, 232221, 134211, 14131231, 14231241, ...
- read the ahead term and also count all events of numbers, provided in order of appearance.
Example: 1, 11, 21, 1211, 3112, 132112, 311322, 232122, 421311, 14123113 ...
The Conway sequence is similar to run-length encoding.
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Why is the sequence referred to as the Conway Sequence?
This sequence has actually been invented and also analyzed by famed mathematician man H. Conway.
See more: How Many Months Have 28 Days In Them, How Many Months Of The Year Have 28 Days
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