Next Look-and-Say Term GeneratorTerm/Number
|Calcul||Next Term Previous Term|
Conway Sequence GeneratorInitial term (seed) Generate
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How does the Conway Sequence works?
To geneprice the next term in the sequence, usage the previous one, by reading it digit by digit and also grouping the numbers that are recurring consecutively. The sequence typically starts through 1 initially term (also called seed).
You are watching: 1 11 21 1211 111221 312211
|21||one 2 and also one 1||1211|
|1211||one 1, one 2 and also 2 1s||111221|
|111221||3 1s, 2 2s and also 1||312211|
The Conmethod 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 likewise well-known as the audioactive suite or look and also say sequence.
The sequence via seed 1 includes just the digits 1, 2 and 3.
All terms begin through 1 or 3 other than the third.
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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 first time at term n, then the term n-1 need to additionally contain 333 (_333 or 333_ can just show up through a series of three 3 in the previous term). Contradiction, the hypothesis is false, so 333 never before shows up.
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What are the variants of the Conway Sequence?
The Conmethod sequence is collection to start 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 acquired is g, 1g, 111g, 311g, 13211g, 111312211g ... (the seed is constantly at the end).
It is possible to use slightly different rules:
- Read the previous term and also count all incidents of numbers, provided in ascending order.
Example: 1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, ...
- Read the previous term and also count all occurrences 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 occurrences of numbers, noted in order of appearance.
Example: 1, 11, 21, 1211, 3112, 132112, 311322, 232122, 421311, 14123113 ...
The Conway sequence is equivalent to run-size encoding.
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Why is the sequence referred to as the Conmethod Sequence?
This sequence has been created and analyzed by well known mathematician John H. Conmeans.
See more: How Many Months Have 28 Days In Them, How Many Months Of The Year Have 28 Days
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