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341 (number)
341 (three hundred ndforty-one) is the natural number following 340 and preceding 342. In mathematics * 341 is the sum of seven consecutive primes (37 + 41 + 43 + 47 + 53 + 59 + 61). * 341 is an octagonal number and a centered cube number. * 341 is a super-Poulet number. * 341 is the smallest Fermat pseudoprime; it is the ''least'' ''composite'' ''odd'' modulus ''m'' greater than the base ''b'', that satisfies the ''Fermat'' property "''bm''−1 − 1 is divisible by ''m''", for bases up to 128 of b = 2, 15, 60, 63, 78, and 108. * 341 is a palindrome in base 2 (1010101012), 4 (111114), 8 (5258), 17 (13117) and 30 (BB30). * 341 is repdigit In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Ex ... in base 4 (111114) and 30 (BB30). References {{Integers, 3 Integers ... [...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] |
340 (number)
300 (three hundred) is the natural number following 299 and preceding 301. In Mathematics 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. Integers from 301 to 399 300s 301 302 303 304 305 306 307 308 309 310s 310 311 312 313 314 315 315 = 32 × 5 × 7 = D_ \!, rencontres number, highly composite odd number, having 12 divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits. 316 316 = 22 × 79, a centered triangular number and a centered heptagonal number. 317 317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 318 319 319 = 11 &t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
342 (number)
300 (three hundred) is the natural number following 299 and preceding 301. In Mathematics 300 is a composite number and the 24th triangular number. It is also a second hexagonal number. Integers from 301 to 399 300s 301 302 303 304 305 306 307 308 309 310s 310 311 312 313 314 315 315 = 32 × 5 × 7 = D_ \!, rencontres number, highly composite odd number, having 12 divisors. It is a Harshad number, as it is divisible by the sum of its digits. It is a Zuckerman number, as it is divisible by the product of its digits. 316 316 = 22 × 79, a centered triangular number and a centered heptagonal number. 317 317 is a prime number, Eisenstein prime with no imaginary part, Chen prime, one of the rare primes to be both right and left-truncatable, and a strictly non-palindromic number. 317 is the exponent (and number of ones) in the fourth base-10 repunit prime. 318 319 319 = 11 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octagonal Number
In mathematics, an octagonal number is a figurate number. The ''n''th octagonal number ''o''''n'' is the number of dots in a pattern of dots consisting of the outlines of regular octagons with sides up to ''n'' dots, when the octagons are overlaid so that they share one vertex (geometry), vertex. The octagonal number for ''n'' is given by the formula 3''n''2 − 2''n'', with ''n'' > 0. The first few octagonal numbers are : 1 (number), 1, 8 (number), 8, 21 (number), 21, 40 (number), 40, 65 (number), 65, 96 (number), 96, 133 (number), 133, 176 (number), 176, 225 (number), 225, 280 (number), 280, 341, 408, 481, 560, 645, 736, 833, 936 The octagonal number for ''n'' can also be calculated by adding the square of ''n'' to twice the (''n'' − 1)th pronic number. Octagonal numbers consistently alternate parity (mathematics), parity. Octagonal numbers are occasionally referred to as "star numbers", though that term is more commonly used to refer to centered dodecagonal numbers. Appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Cube Number
A centered cube number is a centered figurate number that counts the points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has points along each of its edges. The first few centered cube numbers are : 1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, ... . Formulas The centered cube number for a pattern with concentric layers around the central point is given by the formula :n^3 + (n + 1)^3 = (2n+1)\left(n^2+n+1\right). The same number can also be expressed as a trapezoidal number (difference of two triangular numbers), or a sum of consecutive numbers, as :\binom-\binom = (n^2+1)+(n^2+2)+\cdots+(n+1)^2. Properties Because of the factorization , it is impossible for a centered cube number to be a prime number. The only centered cube numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-Poulet Number
In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d divides 2^d - 2. For example, 341 is a super-Poulet number: it has positive divisors (1, 11, 31, 341), and we have: :(211 − 2) / 11 = 2046 / 11 = 186 :(231 − 2) / 31 = 2147483646 / 31 = 69273666 :(2341 − 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550 When \frac is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number. The super-Poulet numbers below 10,000 are : Super-Poulet numbers with 3 or more distinct prime divisors It is relatively easy to get super-Poulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a super-Poulet number, as you built the product of the three prime factors. Example: 2701 = 37 * 73 is a Poulet number, 4033 = 37 * 109 is a Poulet number, 7957 = 73 * 109 is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat Pseudoprime
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Definition Fermat's little theorem states that if p is prime and a is coprime to p, then a^-1 is divisible by p. For a positive integer a, if a composite integer x divides a^-1 then x is called a Fermat pseudoprime to base a. In other words, a composite integer is a Fermat pseudoprime to base a if it successfully passes the Fermat primality test for the base a. The false statement that all numbers that pass the Fermat primality test for base 2 are prime is called the Chinese hypothesis. The smallest base-2 Fermat pseudoprime is 341. It is not a prime, since it equals 11·31, but it satisfies Fermat's little theorem: 2^ \equiv 1 (\bmod) and thus passes the Fermat primality test for the base 2. Pseudoprimes to base 2 are sometimes called Sarrus numbers, after P. F. Sarrus who discovered that 341 has this property, Poulet numbers, after P. Poulet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of "repeated" and "digit". Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes (which are repdigits when represented in binary). Any such number can be represented as follows \underbrace_ = \frac Where nn is the concatenation of n with n. k the number of concatenated n. nn can be represented mathematically as n\cdot\left(10^+1\right) for n = 23 and k = 5, the formula will look like this \frac = \frac = \underbrace_ However, 2323232323 is not a repdigit. Also, any number can be decomposed into the sum and difference of the repdigit numbers. For example 3453455634 = 3333333333 + (111111111 + (99999 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
