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Gijswijt's Sequence
In mathematics, Gijswijt's sequence (named after Dion Gijswijt by Neil Sloane) is a self-describing sequence where each term counts the maximum number of repeated blocks of numbers in the sequence immediately preceding that term. The sequence begins with: : 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 1, ... The sequence is similar in definition to the Kolakoski sequence, but instead of counting the longest run of single terms, the sequence counts the longest run of blocks of terms of any length. Gijswijt's sequence is known for its remarkably slow rate of growth. For example, the first 4 appears at the 220th term, and the first 5 appears near the 10^rd term. Definition The process to generate terms in the sequence can be defined by looking at the sequence as a series of letters in the alphabet of natural numbers: # a(1) = 1, and # a(n+1) = k, where k is the largest natural number such that the word a(1)a(2)a(3)...a(n) can be written in the form xy^k for some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dion Gijswijt
Dion may refer to: People Ancient *Dion (mythology), a king in Laconia and husband of Iphitea, the daughter of Prognaus *Dion of Syracuse (408–354 BC), ancient Greek politician *Dio of Alexandria, first century BC, ancient Greek philosopher *Dion of Naples, an ancient Greek mathematician cited by Augustine of Hippo along with Adrastus of Cyzicus *Dio Chrysostom, also known as Dion Chrysostomos (c. 40 – c. 115), a Greek orator, writer, philosopher and historian *Cassius Dio, also known as Dion Kassios (c. AD 155 – 235), a Roman consul Modern Given name *Dion Bakker (born 1981), Dutch Youtuber and artist *Dion O'Banion, American mobster *Dion Boucicault (1820–1890), Irish actor and playwright * Dion Boucicault Jr. (1859–1929), American actor and stage director *Dion Dawkins (born 1994), American football player *Dion DiMucci (born 1939), American singer/songwriter known professionally as "Dion" *Dion Dublin (born 1969), English footballer *Dion Fortune (1890–1946), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |