Statements (46)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
integer sequence
|
| gptkbp:alsoKnownAs |
Thue-Morse sequence
|
| gptkbp:appearsIn |
number theory
theoretical computer science combinatorics fractal geometry |
| gptkbp:author |
gptkb:N._J._A._Sloane
|
| gptkbp:citation |
Allouche, J.-P.; Shallit, J. (1999), The ubiquitous Prouhet-Thue-Morse sequence, in C. Ding; T. Helleseth; H. Niederreiter (eds.), Sequences and their Applications, Springer, pp. 1–16.
OEIS A001285 OEIS A004718 OEIS A006995 OEIS A010060 OEIS A014601 OEIS A030101 |
| gptkbp:definedIn |
a(n) = number of 1's in binary expansion of n, modulo 2
|
| gptkbp:first_terms |
0
1 |
| gptkbp:form |
a(2n) = a(n)
a(n) = a(floor(n/2)) if n even, 1 - a(floor(n/2)) if n odd a(2n+1) = 1 - a(n) a(n) = sum of binary digits of n mod 2 |
| gptkbp:hasKeyword |
easy
nice core nonn |
| gptkbp:hasProperty |
balanced
aperiodic self-similar cube-free fixed point of morphism 0→01, 1→10 minimal subshift with zero topological entropy not eventually periodic uniformly recurrent |
| https://www.w3.org/2000/01/rdf-schema#label |
OEIS A003107
|
| gptkbp:namedAfter |
gptkb:Marston_Morse
gptkb:Axel_Thue |
| gptkbp:OEIS |
A003107
|
| gptkbp:relatedTo |
gptkb:paperfolding_sequence
automatic sequence cube-free sequence |
| gptkbp:sequence |
binary sequence
automatic sequence cube-free sequence |
| gptkbp:sequenceExample |
0, 1, 1, 0, 1, 0, 0, 1, ...
|
| gptkbp:bfsParent |
gptkb:OEIS_A003215
|
| gptkbp:bfsLayer |
8
|