An alternating factorial is the absolute value of the alternating sum of the first n factorials. This is the same as their sum, with the odd-indexed factorials multiplied by −1 if n is even, and the even-indexed factorials multiplied by −1 if n is odd, resulting in an alternation of signs of the summands (or alternation of addition and subtraction operators, if preferred). To put it algebraically, or with the recurrence relation af(n) = n! − af(n − 1) in whic ...

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• Alternating factorial - Reference

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In mathematics an automorphic number is a number whose square "ends" in the number itself. For example, 52 = 25, 762 = 5776, and 8906252 = 793212890625. The automorphic numbers begin 1, 5, 6, 25, 76, 376, 625, 9376, ... (sequence A003226 in OEIS) Given a k-digit automorphic number n > 1, an at-most 2k-digit automorphic number

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In combinatorial mathematics, the nth Bell number, named in honor of Eric Temple Bell, is the number of partitions of a set with n members, or equivalently, the number of equivalence relations on it. Starting with B0 = B1 = 1, the first few Bell numbers are (sequence A000110 in OEIS): 1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975 (See also breakdown by number of subsets/equivalence classes.) Bell number - Partitions of a set. I ...

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• Bell number - Partitions of a set
• Bell number - Another view of Bell numbers
• Bell number - Properties of Bell numbers
• Bell number - Triangle scheme for calculating Bell numbers

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An alkane in organic chemistry is a saturated hydrocarbon without cycles, that is, an acyclic hydrocarbon in which the molecule has the maximum possible number of hydrogen atoms and so has no double bonds. Alkanes are also often known as paraffins, or collectively as the paraffin series; these terms, however, are also used to apply only to alkanes whose carbon atoms form a single, unbranched chain; when this is done, branched-chain alkanes are called isoparaffins. Alkanes are aliphatic compounds. The general formu ...

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• Alkane - Isomerism
• Alkane - Nomenclature of alkanes
• Alkane - Alkanes with unbranched carbon chains
• Alkane - Alkanes with branched carbon chains
• Alkane - Trivial names
• Alkane - Occurrence
• Alkane - Purification and use
• Alkane - Preparation
• Alkane - Molecular geometry
• Alkane - Bond lengths and bond angles
• Alkane - Conformation
• Alkane - Properties
• Alkane - Physical properties
• Alkane - Chemical properties
• Alkane - Thermochemistry
• Alkane - Spectroscopic properties
• Alkane - Reactions
• Alkane - Reactions with oxygen
• Alkane - Reactions with halogens
• Alkane - Cracking and reforming
• Alkane - Other reactions
• Alkane - Hazards
• Alkane - Alkanes in nature
• Alkane - Bacteria and archaea
• Alkane - Fungi and plants
• Alkane - Animals
• Alkane - Ecological relations

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The mathematical constant π is a real number which may be defined as the ratio of a circle's circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. The name of the Greek letter π is pi (pronounced pie in English), and this spelling can be used in typographical contexts where the Greek letter is not available. π is also known as Archimedes' constant (not to be confused with Archime ...

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• Pi - Properties
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• Pi - Geometry
• Pi - Analysis
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• Pi - Number theory
• Pi - Dynamical systems and ergodic theory
• Pi - Physics
• Pi - Probability and statistics
• Pi - History of π
• Pi - Numerical approximations of π
• Pi - Miscellaneous formulae
• Pi - Less accurate approximations
• Pi - Open questions
• Pi - The nature of π
• Pi - Fictional references
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In mathematics, an abundant number or excessive number is a number n for which σ(n) > 2n. Here σ(n) is the divisor function: the sum of all positive divisors of n, including n itself. The value σ(n) − 2n is called the abundance of n. An equivalent definition is that the proper divisors of the number (the divisors except the number itself) sum to more than the number. The first few abundant numbers (sequence A005101 in OEIS) are: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66 ...

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N is the fourteenth letter of the modern Latin alphabet. Its name in English is en. Semitic Nûn was probably the picture of a snake; the sound value of the letter was /n/ - as in Greek, Etruscan, Latin and all modern languages. Greek name: Nυ, Ny. N - Usage. N serves as an alveolar nasal in virtually all languages that use the Latin alphabet. A common digraph with N is NG, which produces a velar nasal in a variety of languages, usually final in English. Aspirated forms NH and NGH are sometim ...

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• N - Usage
• N - Alternative representations
• N - Computing
• N - Meanings for N

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In 1919 Viggo Brun showed that the sum of the reciprocals of the twin primes (pairs of prime numbers which differ by 2) converges to a mathematical constant now called Brun's constant for twin primes and usually denoted by B2 (sequence A065421 in OEIS): in stark contrast to the fact that the sum of the reciprocals of all primes is divergent. Had this series diverged, we would have a proof of the twin prime conjecture. But since it converges, we do not yet know if there are infinitely many ...

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43 is the natural number following 42 and preceding 44. << 40 41 42 43 44 45 46 47 48 49 >> List of numbers -- Integers 0 10 20 30 40 50 60 70 80 90 >> 43 number - In mathematics. Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, the next is forty-seven. 43 is a centered heptagonal number. 43 is the smallest prime that is not a Chen prime.< ...

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• 43 number - In mathematics
• 43 number - In science
• 43 number - In the periodic table
• 43 number - In astronomy
• 43 number - In other fields

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In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems; which often have a recursive flavour. They are named for the Belgian mathematician Eugène Charles Catalan (1814–1894). The nth Catalan number is given directly in terms of binomial coefficients by Catalan number - Properties of the Catalan numbers. One can verify that an alternative expression for Cn is ...

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• Catalan number - Properties of the Catalan numbers
• Catalan number - Applications in combinatorics
• Catalan number - Proof of the formula
• Catalan number - First proof: using generating functions
• Catalan number - Second proof
• Catalan number - Third proof
• Catalan number - Hankel matrix
• Catalan number - History

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Three hundred is the natural number following two hundred and ninety-nine and preceding three hundred one. << 0 100 200 300 400 500 600 700 800 900 >> 300 number - Mathematical properties. It is a triangular number and the sum of a twin prime (149 + 151), as well as the sum of ten consecutive primes (13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47). It is a Harshad number. 300 number - Other fields. Including:

• 300 number - Mathematical properties
• 300 number - Other fields
• 300 number - Integers from 301 to 399

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An untouchable number is an integer that can not be expressed as the sum of the proper divisors of any integer. The first few untouchable numbers are (sequence A005114 in OEIS): 2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210, 216, 238, 246, 248, 262, 268, 276, 288, 290, 292, 304, 306, 322, 324, 326, 336, 342, 372, 406, 408, 426, 430, 448, 472, 474, 498, 516, 518, 520, 530, 540, 552, 556, 562, 576, 584, 612, 624, 626, 628, 658 5 is believed to be the only odd untouchable number, but this has not been proven. (Thus it ...

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In mathematics, a unique prime is a certain kind of prime number. A prime p ≠ 2, 5 is called unique if there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1 / p, is equivalent to the period length of the reciprocal of q, 1 / q. Unique primes were first described by Samuel Yates in 1980. It can be shown that a prime p is of unique period n iff there exists a nat ...

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In mathematics, a Wilson prime is a certain kind of prime number. A prime p is called a Wilson prime if p² divides (p − 1)! + 1, where ! denotes the factorial function; compare this with Wilson's theorem, which states that every prime p divides (p − 1)! + 1. The only known Wilson primes are 5, 13, and 563 (sequence A007540 in OEIS); if any others exist, they must be greater than 5 · 108. It has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval [x, ...

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In mathematics, a Woodall number is a natural number of the form n · 2n − 1 (written Wn). Woodall numbers were first studied by A. J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers. The first few Woodall numbers are 1, 7, 23, 63, 159, 383, 895, ... (sequence A003261 in OEIS). Wo ...

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In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not. Constructible polygon - Conditions for constructibility. Some regular polygons are easy to construct with compass and straightedge; others are not. This led to the question being posed: is it possible to construct all regular n-gons with compass and straightedge? If not ...

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• Constructible polygon - Conditions for constructibility
• Constructible polygon - General theory
• Constructible polygon - Detailed results in terms of Fermat primes
• Constructible polygon - Compass-and-straightedge constructions
• Constructible polygon - Other constructions

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It has been claimed that the ancient Egyptians knew the golden ratio because ratios close to the golden ratio may be found in the positions or proportions of the Pyramids of Giza. The ancient Greeks already knew the golden ratio from their investigations into geometry, but there is no evidence they thought the number warranted special attention above that for numbers like π (Pi), for example. Studies by psychologists have been devised to test the idea that the golden ratio plays a role in human perception ...

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Golden ratio, Golden ratio - Definition, Golden ratio - History, Golden ratio - A startlingly quick proof of irrationality, Golden ratio - Alternate forms, Golden ratio - Mathematical uses, Golden ratio - Aesthetic uses, Golden ratio - Decimal expansion

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There usually are fewer 2-digit Friedman numbers than 3-digit and more in any given base, but the 2-digit ones are easier to find. If we represent a 2-digit number as mb + n, where b is the base and m, n are integers between -1 and b, we need only check each possible combination of m and n against the equalities mb + n == mn, mb + n == mn, and mb + n == nm to see which ones return true. We ...

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Friedman number, Friedman number - Algorithms for finding Friedman numbers, Friedman number - Friedman numbers using Roman numerals

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Main article: History of Lego Also see: Lego timeline The Lego Group had humble beginnings in the workshop of Ole Kirk Christiansen, a poor carpenter from Billund, Denmark. Ole Kirk started creating wooden toys in 1932, but it wasn't until 1949 that the famous plastic Lego brick was created. The company name Lego was coined by Christiansen from the Danish phrase leg godt, meaning "play well". The Lego Group claims that "Lego" means "I put together" or "I assemble" in Latin, though this is a rather liberal translat ...

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Lego, Lego - Brief history, Lego - The Lego trademark, Lego - Design and manufacture, Lego - Lego today, Lego - Novel applications of Lego, Lego - The Lego system in art, Lego - Trivia, Lego - References and further reading:

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Magic square - The Lo Shu Square 3x3 magic square. Chinese literature dating from as early as 2800 BC tells the legend of Lo Shu or "scroll of the river Lo". In ancient China, there was a huge flood. The people tried to offer some sacrifice to the river god of one of the flooding rivers, the Lo river, to calm his anger. Then, there emerged from the water a turtle with a curious figure/pattern on its shell; there were circular dots of numbers that were arranged in a three by three nine-grid pattern such that the s ...

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Magic square, Magic square - Brief history of magic squares, Magic square - The Lo Shu Square 3x3 magic square, Magic square - The early squares of order four 4x4 magic squares, Magic square - Cultural significance of magic squares, Magic square - Albrecht Dürer's magic square, Magic square - The Sagrada Família magic square, Magic square - Types of magic squares and their construction, Magic square - A method for constructing a magic square of odd order, Magic square - A method of constructing a magic square of doubly even order, Magic square - Counting magic squares, Magic square - Generalizations, Magic square - Extra constraints, Magic square - Different constraints, Magic square - Other operations, Magic square - Other magic shapes, Magic square - Combined extensions, Magic square - Related problems, Magic square - Magic Square of Primes, Magic square - n-Queens problem

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