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226 (number)
226 (two hundred ndtwenty-six) is the natural number following 225 and preceding 227. In mathematics 226 is a happy number, and a semiprime ( 2× 113), and a member of Aronson's sequence. At most 226 different permutation pattern In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation as a sequence of digits representing the result of applying the p ...s can occur within a single 9-element permutation. In other fields * The number of ages Hanako has been alive. References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
225 (number)
225 (two hundred ndtwenty-five) is the natural number following 224 and preceding 226. In mathematics 225 is the smallest number that is a polygonal number in five different ways. It is a square number , an octagonal number, and a squared triangular number . As the square of a double factorial, counts the number of permutations of six items in which all cycles have even length, or the number of permutations in which all cycles have odd length. And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles. 225 is a highly composite odd number, meaning that it has more divisors than any smaller odd numbers. After 1 and 9, 225 is the third smallest number ''n'' for which , where ''σ'' is the sum of divisors function and ''φ'' is Euler's totient function. 225 is a refactorable number. 225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4) 225 is the fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
227 (number)
227 (two hundred ndtwenty-seven) is the natural number between 226 and 228. It is also a prime number. In mathematics 227 is a twin prime and the start of a prime triplet (with 229 and 233). It is a safe prime, as dividing it by two and rounding down produces the Sophie Germain prime 113. It is also a regular prime, a Pillai prime, a Stern prime, and a Ramanujan prime. 227 and 229 form the first twin prime pair for which neither is a cluster prime. The 227th harmonic number is the first to exceed six. There are 227 different connected graphs with eight edges, and 227 independent sets in a 3 × 4 grid graph In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space , forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a latti .... References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Happy Number
In number theory, a happy number is a number which eventually reaches 1 when 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 digital invaria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime numbers, there are also infinitely many semiprimes. Semiprimes are also called biprimes. Examples and variations The semiprimes less than 100 are: Semiprimes that are not square numbers are called discrete, distinct, or squarefree semiprimes: The semiprimes are the case k=2 of the k-almost primes, numbers with exactly k prime factors. However some sources use "semiprime" to refer to a larger set of numbers, the numbers with at most two prime factors (including unit (1), primes, and semiprimes). These are: Formula for number of semiprimes A semiprime counting formula was discovered by E. Noel and G. Panos in 2005. Let \pi_2(n) denote the number of semiprimes less than or equal to n. Then \pi_2(n) = \sum_^ pi(n/p_k) - k + 1 /math> where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
113 (number)
113 (one hundred ndthirteen) is the natural number following 112 and preceding 114. Mathematics * 113 is the 30th prime number (following 109 and preceding 127), so it can only be divided by one and itself. 113 is a Sophie Germain prime, an emirp, an isolated prime, a Chen prime and a Proth prime as it is a prime number of the form 7 × 24 + 1. 113 is also an Eisenstein prime with no imaginary part and real part of the form 3n - 1. In base 10, this prime is a primeval number, and a permutable prime with 131 and 311. *113 is a highly cototient number and a centered square number. *113 is the denominator of 355/113, an accurate approximation to . See also * 113 (other) * A113 is A Pixar recurring inside joke or Easter Egg, e.g.: (WALL-E) = (W-A113). References * Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers ''The Penguin Dictionary of Curious and Interesting Numbers'' is a reference book for recreational mathematics and elementary n ... [...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 occurs in natural or formal langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation. Any permutation may be written in one-line notation as a sequence of digits representing the result of applying the permutation to the digit sequence 123...; for instance the digit sequence 213 represents the permutation on three elements that swaps elements 1 and 2. If π and σ are two permutations represented in this way (these variable names are standard for permutations and are unrelated to the number pi), then π is said to ''contain'' σ as a ''pattern'' if some subsequence of the digits of π has the same relative order as all of the digits of σ. For instance, permutation π contains the pattern 213 whenever π has three digits ''x'', ''y'', and ''z'' that appear within π in the order ''x''...''y''...''z'' but whose values are ordered as ''y'' < ''x'' < ''z'', the same as the ordering of the values in the permutation 213. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanako (fish)
Hanako ( c. 1751 – July 7, 1977) was a scarlet koi fish owned by several individuals, the last of whom was Dr. Komei Koshihara. The name translates to "flower child" in Japanese. Far exceeding the average lifespan for her breed, she was reportedly 226 years old at the time of her death. Her age was determined in 1966 by removing two of her scales and examining them extensively. At this time, Hanako weighed and measured in length. Once the scales were fully analyzed, it was determined that she was 215 years old. In July 1974, a study of the growth rings of one of the koi's scales reported that Hanako was 226 years old. She may be, to date, the longest-lived koi fish ever recorded. There has been a dispute as to the veracity of these longevity claims. The average koi bred outside of Japan can be expected to reach 15 years of age, while the average Japanese koi's lifespan is 40 years. Some sources give an accepted age for the species at little more than 50 years. See also *List ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
