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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] |
