|
Kolakoski Sequence
In mathematics, the Kolakoski sequence, sometimes also known as the Oldenburger–Kolakoski sequence, is an infinite sequence of symbols that is the sequence of run lengths in its own run-length encoding. It is named after the recreational mathematician William Kolakoski (1944–97) who described it in 1965, but it was previously discussed by Rufus Oldenburger in 1939. Definition The initial terms of the Kolakoski sequence are: :1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,... Each symbol occurs in a "run" (a sequence of equal elements) of either one or two consecutive terms, and writing down the lengths of these runs gives exactly the same sequence: :1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,2,2,... :1, 2 , 2 ,1,1, 2 ,1, 2 , 2 ,1, 2 , 2 ,1,1, 2 ,1,1, 2 , 2 ,1, 2 ,1,1, 2 ,1, 2 , 2&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Complete
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence. Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Sequences
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified ''explicitly'' by giving a formula for its ''n''th term, or ''implicitly'' by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula ''n''2 − 1 for the ''n''th term: an explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the ''n''th perfect number. Examples Integer sequences that have their own name include: *Abundant numbers *Baum–Sweet sequence *Bell numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brady Haran
Brady John Haran (born 18 June 1976) is an Australian-British independent filmmaker and video journalist who produces educational videos and documentary films for his YouTube channels, the most notable being ''Periodic Videos'' and ''Numberphile''. Haran is also the co-host of the'' Hello Internet'' podcast along with fellow educational YouTuber CGP Grey. On 22 August 2017, Haran launched his second podcast, called ''The Unmade Podcast'', and on 11 November 2018, he launched his third podcast, '' The Numberphile Podcast'', based on his mathematics-centered channel of the same name. Reporter and filmmaker Brady Haran studied journalism for a year before being hired by ''The Adelaide Advertiser''. In 2002, he moved from Australia to Nottingham, United Kingdom. In Nottingham, he worked for the BBC, began to work with film, and reported for ''East Midlands Today'', BBC News Online and BBC radio stations. In 2007, Haran worked as a filmmaker-in-residence for Nottingham Science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. See also * ''Bulletin of the American Mathematical Society'' * '' Journal of the American Mathematical Society'' * ''Memoirs of the American Mathematical Society'' * ''Notices of the American Mathematical Society'' * ''Proceedings of the American Mathematical Society'' External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ... American Mathematical Society academic journals Mathematics journals Publications established in 1900 {{math-journal-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Look-and-say Sequence
In mathematics, the look-and-say sequence is the integer sequence, sequence of integers beginning as follows: : 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, 31131211131221, ... . To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example: * 1 is read off as "one 1" or 11. * 11 is read off as "two 1s" or 21. * 21 is read off as "one 2, one 1" or 1211. * 1211 is read off as "one 1, one 2, two 1s" or 111221. * 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Horton Conway, John Conway Reprinted as after he was introduced to it by one of his students at a party. The idea of the look-and-say sequence is similar to that of run-length encoding. If started with any digit ''d'' from 0 to 9 then ''d'' will remain indefinitely as the last digit of the sequence. For any ''d'' other than 1, the sequence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golomb Sequence
In mathematics, the Golomb sequence, named after Solomon W. Golomb (but also called Silverman's sequence), is a monotonically increasing integer sequence where ''an'' is the number of times that ''n'' occurs in the sequence, starting with ''a''1 = 1, and with the property that for ''n'' > 1 each ''an'' is the smallest unique integer which makes it possible to satisfy the condition. For example, ''a''1 = 1 says that 1 only occurs once in the sequence, so ''a''2 cannot be 1 too, but it can be, and therefore must be, 2. The first few values are :1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12 . Examples ''a''1 = 1 Therefore, 1 occurs exactly one time in this sequence. ''a''2 > 1 ''a''2 = 2 2 occurs exactly 2 times in this sequence. ''a''3 = 2 3 occurs exactly 2 times in this sequence. ''a''4 = ''a''5 = 3 4 occurs exactly 3 times in this sequence. 5 occurs exactly 3 times in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
L (complexity)
In computational complexity theory, L (also known as LSPACE or DLOGSPACE) is the complexity class containing decision problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space., Definition 8.12, p. 295., p. 177. Formally, the Turing machine has two tapes, one of which encodes the input and can only be read, whereas the other tape has logarithmic size but can be read as well as written. Logarithmic space is sufficient to hold a constant number of pointers into the input and a logarithmic number of boolean flags, and many basic logspace algorithms use the memory in this way. Complete problems and logical characterization Every non-trivial problem in L is complete under log-space reductions, so weaker reductions are required to identify meaningful notions of L-completeness, the most common being first-order reductions. A 2004 result by Omer Reingold shows that USTCON, the problem of whether there exists a path ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
