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141 (number)
141 (one hundred [and] forty-one) is the natural number following 140 (number), 140 and preceding 142 (number), 142. In mathematics 141 is: *a centered pentagonal number. *the sum of the sums of the divisors of the first 13 positive integers. *the second ''n'' to give a prime Cullen number (of the form ''n''2''n'' + 1). *an undulating number in base 10, with the previous being 131 (number), 131, and the next being 151 (number), 151. *the sixth hendecapolygonal number, gonal (11-gonal) number. *a semiprime: a product of two prime numbers, namely 3 and 47. Since those prime factors are Gaussian primes, this means that 141 is a Blum integer. * a Hilbert number, Hilbert prime References [...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] |
140 (number)
140 (one hundred [and] forty) is the natural number following 139 (number), 139 and preceding 141 (number), 141. In mathematics 140 is an abundant number and a harmonic divisor number. It is the sum of the squares of the first seven integers, which makes it a square pyramidal number. 140 is an odious number because it has an odd number of ones in its binary representation. The sum of Euler's totient function φ(''x'') over the first twenty-one integers is 140. 140 is a repdigit in bases 13, 19, 27, 34, 69, and 139. In other fields 140 is also: * The former Twitter entry-character limit, a well-known characteristic of the service (based on the text messaging limit) ** A film, based on the Twitter entry-character limit, created and edited by Frank Kelly of Ireland References External links The Natural Number 140 {{DEFAULTSORT:140 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
142 (number)
142 (one hundred ndforty-two) is the natural number following 141 and preceding 143. In mathematics There are 142 connected functional graphs on four labeled vertices, 142 planar graphs with 6 unlabeled vertices, and 142 partial involutions on five elements. It is also palindromic in base 3 (12021). ''In memoriam'' At the United States Merchant Marine Academy The United States Merchant Marine Academy (USMMA or Kings Point) is a United States service academies, United States service academy in Kings Point, New York. It trains its midshipman, midshipmen (as students at the academy are called) to serv ..., the number '142' represents 142 Cadet/Midshipmen who died aboard merchant vessels during World War II. The U.S. Merchant Marine Academy, among the nation's five federal academies, is the only institution authorized to carry battle standardas part of its color guard. The battle standard bears the number "142" on a field of red, white and blue. References Integers< ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Pentagonal Number
In mathematics, a centered pentagonal number is a centered polygonal number, centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the formula :P_=, n\geq1 The first few centered pentagonal numbers are 1 (number), 1, 6 (number), 6, 16 (number), 16, 31 (number), 31, 51 (number), 51, 76 (number), 76, 106 (number), 106, 141 (number), 141, 181 (number), 181, 226 (number), 226, 276 (number), 276, 331 (number), 331, 391 (number), 391, 456 (number), 456, 526 (number), 526, 601 (number), 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 . Properties *The parity of centered pentagonal numbers follows the pattern odd-even-even-odd, and in base 10 the units follow the pattern 1-6-6-1. *Centered pentagonal numbers follow the following recurrence relations: :P_=P_+5n , P_0=1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positive Integers
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 jersey numbers on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cullen Number
In mathematics, a Cullen number is a member of the integer sequence C_n = n \cdot 2^n + 1 (where n is a natural number). Cullen numbers were first studied by James Cullen in 1905. The numbers are special cases of Proth numbers. Properties In 1976 Christopher Hooley showed that the natural density of positive integers n \leq x for which ''C''''n'' is a prime is of the order ''o''(''x'') for x \to \infty. In that sense, almost all Cullen numbers are composite. Hooley's proof was reworked by Hiromi Suyama to show that it works for any sequence of numbers ''n''·2''n'' + ''a'' + ''b'' where ''a'' and ''b'' are integers, and in particular also for Woodall numbers. The only known Cullen primes are those for ''n'' equal to: : 1, 141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899, 1354828, 6328548, 6679881 . Still, it is conjectured that there are infinitely many Cullen primes. A Cullen number ''C''''n'' is divisible by ''p'' = 2''n'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 number theory written by David Wells. The first edition was published in paperback by Penguin Books in 1986 in the UK, and a revised edition appeared in 1997 (). Contents The entries are arranged in increasing order of magnitude, with the exception of the first entry on −1 and ''i''. The book includes some irrational numbers below 10 but concentrates on integers, and has an entry for every integer up to 42. The final entry is for Graham's number. In addition to the dictionary itself, the book includes a list of mathematicians in chronological sequence (all born before 1890), a short glossary, and a brief bibliography. The back of the book contains eight short tables "for the benefit of readers who cannot wait to look for their own patterns and properties", including lists of polygonal numbers, Fibonacci numbers, prime numbers, factorials, decimal r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
131 (number)
131 (one hundred thirty one) is the natural number following 130 (number), 130 and preceding 132 (number), 132. In mathematics 131 is a Sophie Germain prime, an irregular prime, the second 3-digit palindromic prime, and also a permutable prime with 113 (number), 113 and 311 (number), 311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is an Eisenstein prime with no imaginary part and real part of the form 3n - 1. Because the next odd number, 133, is a semiprime, 131 is a Chen prime. 131 is an Ulam number. 131 is a full reptend prime in radix, base 10 (and also in base 2). The decimal expansion of 1/131 repeats the digits 007633587786259541984732824427480916030534351145038167938931 297709923664122137404580152671755725190839694656488549618320 6106870229 indefinitely. 131 is the fifth discriminant of imaginary quadratic fields with class number 5, where the 131st prime number 739 is the fifteenth such discriminant. Meanwhile, there are conjecture ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
151 (number)
151 (one hundred ndfifty-one) is a natural number. It follows 150 and precedes 152. In mathematics 151 is the 36th prime number, the previous is 149, with which it comprises a twin prime. 151 is also a palindromic prime, a centered decagonal number, and a lucky number. 151 appears in the Padovan sequence, preceded by the terms 65, 86, 114; it is the sum of the first two of these. 151 is a unique prime in base 2, since it is the only prime with period 15 in base 2. There are 151 4-uniform tilings, such that the symmetry of tilings with regular polygons have four orbits of vertices. 151 is the number of uniform paracompact honeycombs with infinite facets and vertex figures in the third dimension, which stem from 23 different Coxeter groups. Split into two whole numbers, 151 is the sum of 75 and 76, both relevant numbers in Euclidean and hyperbolic 3-space: * 75 is the total number of non-prismatic uniform polyhedra, which incorporate regular polyhedra, semiregul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygonal Number
In mathematics, a polygonal number is a Integer, number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate numbers. Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of Pronic number, oblong, Triangular Number, triangular, and Square number, square numbers. Definition and examples The number 10 for example, can be arranged as a triangle (see triangular number): : But 10 cannot be arranged as a square (geometry), square. The number 9, on the other hand, can be (see square number): : Some numbers, like 36, can be arranged both as a square and as a triangle (see square triangular number): : By convention, 1 is the first polygonal number for any number of sides. The rule for enlarging the polygon to the next size is to extend two adjacent arms by one point and to then add the required extra sides between those points. In the following diagrams, ... [...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, since they include two primes, or second numbers, by analogy with how "prime" means "first". Alternatively non-prime semiprimes are called almost-prime numbers, specifically the "2-almost-prime" biprime and "3-almost-prime" triprime 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: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
