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.

Observed surface forms (4)

Surface form	As subject	As object
Conway constant	0	2
A005150	0	1
Conway sequence	0	1
look and say sequence	0	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.

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 → 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

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

this entity surface form: A005150

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