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208 (number)
208 (two hundred ndeight) is the natural number following 207 and preceding 209. 208 is a practical number, a tetranacci number, a rhombic matchstick number, a happy number, and a member of Aronson's sequence. There are exactly 208 five-bead necklaces A necklace is an article of jewellery that is worn around the neck. Necklaces may have been one of the earliest types of adornment worn by humans. They often serve Ceremony, ceremonial, Religion, religious, magic (illusion), magical, or Funerar ... drawn from a set of beads with four colors, and 208 generalized weak orders on three labeled points.. References Integers {{Number-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
207 (number)
207 (two hundred ndseven) is the natural number following 206 and preceding 208. It is an odd composite number with a prime factorization of 3^2\cdot 23. In Mathematics * 207 is a Wedderburn-Etherington number. * There are exactly 207 different matchstick graphs with eight edges. * 207 is a deficient number, as 207's proper divisors (divisors not including the number itself) only add up to 105 105 may refer to: *105 (number), the number * AD 105, a year in the 2nd century AD * 105 BC, a year in the 2nd century BC * 105 (telephone number), the emergency telephone number in Mongolia * 105 (MBTA bus), a Massachusetts Bay Transport Authority ...: 1+3+9+23+69=105<207. References Malls Integers {{Number-stub ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
209 (number)
209 (two hundred ndnine) is the natural number following 208 and preceding 210. In mathematics *There are 209 spanning trees in a 2 × 5 grid graph, 209 partial permutations on four elements, and 209 distinct undirected simple graphs on 7 or fewer unlabeled vertices. *209 is the smallest number with six representations as a sum of three positive squares. These representations are: *:209 . :By Legendre's three-square theorem, all numbers congruent to 1, 2, 3, 5, or 6 mod 8 have representations as sums of three squares, but this theorem does not explain the high number of such representations for 209. *, one less than the product of the first four prime numbers. Therefore, 209 is a Euclid number of the second kind, also called a Kummer number. One standard proof of Euclid's theorem Euclid's theorem is a fundamental statement in number theory that asserts that there are Infinite set, infinitely many prime number, prime numbers. It was first proven by Euclid in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Practical Number
In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5 = 3 + 2, 7 = 6 + 1, 8 = 6 + 2, 9 = 6 + 3, 10 = 6 + 3 + 1, and 11 = 6 + 3 + 2. The sequence of practical numbers begins Practical numbers were used by Fibonacci in his ''Liber Abaci'' (1202) in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators.. The name "practical number" is due to . He noted that "the subdivisions of money, weights, and measures involve numbers like 4, 12, 16, 20 and 28 which are usually supposed to be so inconvenient as to d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetranacci Number
In mathematics, the Fibonacci numbers form a sequence defined recursively by: :F_n = \begin 0 & n = 0 \\ 1 & n = 1 \\ F_ + F_ & n > 1 \end That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers. Extension to negative integers Using F_ = F_n - F_, one can extend the Fibonacci numbers to negative integers. So we get: :... −8, 5, −3, 2, −1, 1, 0, 1, 1, 2, 3, 5, 8, ... and F_ = (-1)^ F_n. See also Negafibonacci coding. Extension to all real or complex numbers There are a number of possible generalizations of the Fibonacci numbers which include the real numbers (and sometimes the complex numbers) in their domain. These each involve the golden ratio , and are based on Binet's formula :F_n = \frac. The ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Happy Number
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aronson's Sequence
Aronson's sequence is an integer sequence defined by the English sentence "T is the first, fourth, eleventh, sixteenth, ... letter in this sentence." Spaces and punctuation are ignored. The first few numbers in the sequence are: :1, 4, 11, 16, 24, 29, 33, 35, 39, 45, 47, 51, 56, 58, 62, 64, 69, 73, 78, 80, 84, 89, 94, 99, 104, 111, 116, 122, 126, 131, 136, 142, 147, 158, 164, 169, ... . In Douglas Hofstadter's book '' Metamagical Themas'', the sequence is credited to Jeffrey Aronson of Oxford, England. The sequence is infinite—and this statement requires some proof. The proof depends on the observation that the English names of all ordinal numbers, except those that end in 2, must contain at least one "t".. Aronson's sequence is closely related to autograms. There are many generalizations of Aronson's sequence and research into the topic is ongoing. write that Aronson's sequence is "a classic example of a self-referential Self-reference is a concept that involves refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necklace (combinatorics)
In combinatorics, a ''k''-ary necklace of length ''n'' is an equivalence class of ''n''-character strings over an alphabet of size ''k'', taking all rotations as equivalent. It represents a structure with ''n'' circularly connected beads which have ''k'' available colors. A ''k''-ary bracelet, also referred to as a turnover (or free) necklace, is a necklace such that strings may also be equivalent under reflection. That is, given two strings, if each is the reverse of the other, they belong to the same equivalence class. For this reason, a necklace might also be called a fixed necklace to distinguish it from a turnover necklace. Formally, one may represent a necklace as an orbit of the cyclic group acting on ''n''-character strings over an alphabet of size ''k'', and a bracelet as an orbit of the dihedral group. One can count these orbits, and thus necklaces and bracelets, using Pólya's enumeration theorem. Equivalence classes Number of necklaces There are :N_k(n) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
