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Happy Numbers (video Game)
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because the sequence starting with 4^2=16 and 1^2+6^2=37 eventually reaches 2^2+0^2=4, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy. More generally, a b-happy number is a natural number in a given number base b that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2. The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia" . Happy numbers and perfect d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harshad Number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers. Because being a Harshad number is determined based on the base the number is expressed in, a number can be a Harshad number many times over. So-called Trans-Harshad numbers are Harshad numbers in every base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit ' (joy) + ' (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. Definition Stated mathematically, let be a positive integer with digits when written in base , and let the digits be a_i (i = 0, 1, \ldots, m-1). (It follows that a_i must be either zero or a positive integer up to .) can be expressed as :X=\sum_^ a_i n^i. is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base 6
A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like the decimal base 10, the base is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to the senary system. Formal definition The standard set of digits in the senary system is \mathcal_6 = \lbrace 0, 1, 2, 3, 4, 5\rbrace, with the linear order 0 < 1 < 2 < 3 < 4 < 5. Let be the of , where is the operation of string concatenation [...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, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lucky Number
In number theory, a lucky number is a natural number in a set which is generated by a certain " sieve". This sieve is similar to the sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers). The term was introduced in 1956 in a paper by Gardiner, Lazarus, Metropolis and Ulam. In the same work they also suggested calling another sieve, "the sieve of Josephus Flavius" because of its similarity with the counting-out game in the Josephus problem. Lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There are infinitely many lucky numbers. Twin lucky numbers and twin primes also appear to occur with similar frequency. However, if ''L''''n'' denotes the ''n''-th lucky number, and ''p''''n'' the ''n''-th prime, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fortunate Number
In number theory, a Fortunate number, named after Reo Fortune, is the smallest integer ''m'' > 1 such that, for a given positive integer ''n'', ''p''''n''# + ''m'' is a prime number, where the primorial ''p''''n''# is the product of the first ''n'' prime numbers. For example, to find the seventh Fortunate number, one would first calculate the product of the first seven primes (2, 3, 5, 7, 11, 13 and 17), which is 510510. Adding 2 to that gives another even number, while adding 3 would give another multiple of 3. One would similarly rule out the integers up to 18. Adding 19, however, gives 510529, which is prime. Hence 19 is a Fortunate number. The Fortunate number for ''p''''n''# is always above ''p''''n'' and all its divisors are larger than ''p''''n''. This is because ''p''''n''#, and thus ''p''''n''# + ''m'', is divisible by the prime factors of ''m'' not larger than ''p''''n''. If a composite Fortunate number does exist, it must be greater than or equal to ''p''''n+1''2. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Dynamics
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory. Part of the inspiration comes from complex dynamics, the study of the Iterated function, iteration of self-maps of the complex plane or other complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer point, integer, rational point, rational, p-adic number, -adic, or algebraic points under repeated application of a polynomial or rational function. A fundamental goal is to describe arithmetic properties in terms of underlying geometric structures. ''Global arithmetic dynamics'' is the study of analogues of classical diophantine geometry in the setting of discrete dynamical systems, while ''local arithmetic dynamics'', also called p-adic dynamics, p-adic or nonarchimedean dynamics, is an analogue of complex dynamics in which one replaces the complex numbers by a -adic field such as or and studies chaotic behavior and the Fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
42 (Doctor Who)
"42" is the seventh episode of the third series of British science fiction television series ''Doctor Who''. It was first broadcast on BBC One on 19 May 2007. It was the first episode written by Chris Chibnall, the showrunner and lead writer of ''Doctor Who'' from series 11 to the 2022 specials. Separated from the TARDIS, the Doctor and Martha face a race against time as they and the crew of the SS Pentallion try to escape from the damaged spaceship before it falls into a nearby star. Meanwhile, a mysterious entity roams the ship. According to the BARB figures this episode was seen by 7.41 million viewers and was the third most popular non-soap-opera broadcast on British television in that week. Plot The Tenth Doctor and Martha receive a distress signal from the SS ''Pentallian'', a human spacecraft that is hurtling towards the star of the Torajii system. The Doctor pilots the TARDIS towards it to help, but after arriving they are separated from the TARDIS by the rising tempe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Who
''Doctor Who'' is a British science fiction television series broadcast by the BBC since 1963. The series, created by Sydney Newman, C. E. Webber and Donald Wilson (writer and producer), Donald Wilson, depicts the adventures of an extraterrestrial being called the Doctor, part of a humanoid species called Time Lords. The Doctor travels in the universe and in time using a time travelling Spacecraft, spaceship called the TARDIS, which externally appears as a British police box. While travelling, the Doctor works to save lives and liberate oppressed peoples by combating List of Doctor Who villains, foes. The Doctor usually travels with Companion (Doctor Who), companions. Beginning with William Hartnell, List of actors who have played the Doctor, fourteen actors have headlined the series as the Doctor; the most recent being Ncuti Gatwa, who portrayed the Fifteenth Doctor from 2023 to 2025. The transition between actors is written into the plot of the series with the Regeneration ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Professor Layton And The Diabolical Box
''Professor Layton and the Diabolical Box'', known in Australia and Europe as ''Professor Layton and Pandora's Box'', is the second game in the ''Professor Layton'' series by Level-5. It was followed by a third game, '' Professor Layton and the Unwound Future''. The game follows Professor Layton and his self-proclaimed apprentice Luke as they travel cross-country by train to solve the mystery behind a mysterious box that is said to kill anyone who opens it. An enhanced mobile port of ''Diabolical Box'', subtitled "HD for Mobile", was released on December 5, 2018. Gameplay ''Professor Layton and the Diabolical Box'' is an adventure/puzzle game. The player controls the movements of the eponymous Professor Layton and his young assistant Luke through several locations, unlike in the previous game which is confined to just one town. Along with completing many different types of puzzles, players must explore different areas, solve mysteries, and aid the Professor on his quest. The pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycle Detection
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function that maps a finite set to itself, and any initial value in , the sequence of iterated function values : x_0,\ x_1=f(x_0),\ x_2=f(x_1),\ \dots,\ x_i=f(x_),\ \dots must eventually use the same value twice: there must be some pair of distinct indices and such that . Once this happens, the sequence must continue periodically, by repeating the same sequence of values from to . Cycle detection is the problem of finding and , given and . Several algorithms are known for finding cycles quickly and with little memory. Robert W. Floyd's tortoise and hare algorithm moves two pointers at different speeds through the sequence of values until they both point to equal values. Alternatively, Brent's algorithm is based on the idea of exponential search. Both Floyd's and Brent's algorithms use only a constant number of memor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base 12
The duodecimal system, also known as base twelve or dozenal, is a positional notation, positional numeral system using 12 (number), twelve as its radix, base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 1, units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve square (algebra), squared (144), "1,000" means twelve cube (algebra), cubed (1,728), and "0.1" means a twelfth (0.08333...). Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses and , as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , and finally 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: (a turned 2) for ten (dek, pronounced dɛk) and 3 (a turned 3) for eleven (el, pron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
