Look-and-say sequence

E29421

combinatorial object integer sequence recursively defined sequence

The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.

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All labels observed (5)

Label	Occurrences
Conway constant	2
A005150	1
Conway sequence	1
Look-and-say sequence canonical	1
look and say sequence	1

Statements (47)

Predicate	Object
instanceOf	combinatorial object ⓘ integer sequence ⓘ recursively defined sequence ⓘ
alsoKnownAs	Look-and-say sequence ⓘ surface form: Conway sequence Look-and-say sequence ⓘ surface form: look and say sequence
definedByRule	each term describes the digits of the previous term in order of appearance ⓘ
growthConstantName	Look-and-say sequence self-linksurface differs ⓘ surface form: Conway constant
hasApproximateConwayConstant	1.303577269034 ⓘ
hasAsymptoticBehavior	length of nth term grows like lambda^n where lambda is the Conway constant ⓘ
hasCombinatorialStructure	decomposes into irreducible subsequences called atoms ⓘ
hasConstructionMethod	start with a seed term and iteratively describe runs of identical digits ⓘ
hasDescriptionLanguage	English digit names and counts ⓘ
hasDigitAlphabet	1 ⓘ 2 ⓘ 3 ⓘ
hasExampleTerm	1113213211 ⓘ 13112221 ⓘ 312211 ⓘ
hasFifthTerm	111221 ⓘ
hasFirstTerm	1 ⓘ
hasFourthTerm	1211 ⓘ
hasGeneralization	look-and-say sequences in other bases ⓘ look-and-say sequences using other symbol alphabets ⓘ
hasGrowthRate	approximately 1.303577269 ⓘ
hasMathematicalArea	combinatorics ⓘ discrete mathematics ⓘ number theory ⓘ
hasNamedConstant	Look-and-say sequence self-linksurface differs ⓘ surface form: Conway constant
hasOEISId	Look-and-say sequence self-linksurface differs ⓘ surface form: A005150
hasProperty	admits a finite set of irreducible elements under the evolution rule ⓘ different seeds lead to different look-and-say sequences ⓘ digits eventually stabilize to a finite set of allowed blocks ⓘ local patterns evolve independently in the limit ⓘ no term contains the digit 4 or higher when written in standard form ⓘ sequence is not eventually periodic ⓘ terms do not converge in value but lengths diverge to infinity ⓘ terms grow in length roughly exponentially ⓘ
hasSecondTerm	11 ⓘ
hasThirdTerm	21 ⓘ
isDescribedIn	On Numbers and Games ⓘ
isFamousFor	nontrivial asymptotic growth analysis by Conway ⓘ unexpected regularities in digit patterns ⓘ
isRelatedTo	cellular automata ⓘ formal languages ⓘ run-length encoding ⓘ
studiedBy	John H. Conway ⓘ surface form: John Horton Conway
typicalSeed	1 ⓘ

Referenced by (6)

Full triples — surface form annotated when it differs from this entity's canonical label.

John H. Conway → notableWork → Look-and-say sequence ⓘ

Look-and-say sequence → alsoKnownAs → Look-and-say sequence ⓘ

this entity surface form: look and say sequence

Look-and-say sequence → alsoKnownAs → Look-and-say sequence ⓘ

this entity surface form: Conway sequence

Look-and-say sequence → hasOEISId → Look-and-say sequence self-linksurface differs ⓘ

this entity surface form: A005150

Look-and-say sequence → growthConstantName → Look-and-say sequence self-linksurface differs ⓘ

this entity surface form: Conway constant

Look-and-say sequence → hasNamedConstant → Look-and-say sequence self-linksurface differs ⓘ

this entity surface form: Conway constant