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874 (number)
800 (eight hundred) is the natural number following 799 and preceding 801. It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number, an Achilles number and the area of a square with diagonal 40. Integers from 801 to 899 800s * 801 = 32 × 89, Harshad number, number of clubs patterns appearing in 50 × 50 coins * 802 = 2 × 401, sum of eight consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, happy number, sum of 4 consecutive triangular numbers (171 + 190 + 210 + 231) * 803 = 11 × 73, sum of three consecutive primes (263 + 269 + 271), sum of nine consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), Harshad number, number of partitions of 34 into Fibonacci parts * 804 = 22 × 3 × 67, nontotient, Harshad number, refactorable number ** "The 804" is a local nickname for the Greater Richmond Region of the U.S. state of Virginia, derived from its telephone area code (although the area code covers a larg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Armenian Numerals
Armenian numerals form a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet. There was no notation for zero in the old system, and the numeric values for individual letters were added together. The principles behind this system are the same as for the ancient Greek numerals and Hebrew numerals. In modern Armenia, the familiar Arabic numerals are used. In contemporary writing, Armenian numerals are used more or less like Roman numerals in modern English, e.g. Գարեգին Բ. means Garegin II and Գ. գլուխ means ''Chapter III'' (as a headline). The final two letters of the Armenian alphabet, "o" (Օ) and "fe" (Ֆ), were added to the Armenian alphabet only after Arabic numerals were already in use, to facilitate transliteration of other languages. Thus, they sometimes have a numerical value assigned to them. Notation As in Hebrew and ancient notation, in Armenian numerals distinct symbols represent multiples of po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strobogrammatic Number
A strobogrammatic number is a number whose numeral is rotationally symmetric, so that it Centrosymmetry, appears the same when rotated 180 degrees. In other words, the numeral looks the same right-side up and upside down (e.g., 69, 96, 1001). A strobogrammatic prime is a strobogrammatic number that is also a prime number, i.e., a number that is only divisible by one and itself (e.g., 11). It is a type of ambigram, words and numbers that retain their meaning when viewed from a different perspective, such as palindromes. Description When written using standard characters (ASCII), the numbers, 0, 1, 8 are symmetrical around the horizontal axis, and 6 and 9 are the same as each other when rotated 180 degrees. In such a system, the first few strobogrammatic numbers are: 0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, 916, 986, 1001, 1111, 1691, 1881, 1961, 6009, 6119, 6699, 6889, 6969, 8008, 8118, 8698, 8888, 8968, 9006, 9116, 9696, 9886, 9966, ... The f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Pyramidal Number
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid (geometry), pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes. As well as counting spheres in a pyramid, these numbers can be described algebraically as a sum of the first n positive square numbers, or as the values of a cubic polynomial. They can be used to solve several other counting problems, including counting squares in a square grid and counting acute triangles formed from the vertices of an odd regular polygon. They equal the sums of consecutive tetrahedral numbers, and are one-fourth of a larger tetrahedral number. The sum of two consecutive square pyramidal numbers is an octahedral number. History The pyramidal numbers were one of the few types of three-dimensional fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Hexagonal Number
In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered polygonal number, centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal numbers: : Centered hexagonal numbers should not be confused with hexagonal number, cornered hexagonal numbers, which are figurate numbers in which the associated hexagons share a vertex. The sequence of hexagonal numbers starts out as follows : :1, 7, 19 (number), 19, 37 (number), 37, 61 (number), 61, 91 (number), 91, 127 (number), 127, 169 (number), 169, 217 (number), 217, 271 (number), 271, 331 (number), 331, 397 (number), 397, 469, 547, 631, 721, 817, 919. Formula The th centered hexagonal number is given by the formula :H(n) = n^3 - (n-1)^3 = 3n(n-1)+1 = 3n^2 - 3n +1. \, Expressing the formula as :H(n) = 1+6\left(\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Padovan Sequence
In number theory, the Padovan sequence is the integer sequence, sequence of integers ''P''(''n'') defined. by the initial values P(0) = P(1) = P(2) = 1, and the recurrence relation P(n) = P(n-2)+P(n-3). The first few values of ''P''(''n'') are :1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, ... The Padovan sequence is named after Richard Padovan who attributed its discovery to Netherlands, Dutch architect Hans van der Laan in his 1994 essay ''Dom. Hans van der Laan: Modern Primitive''.Richard Padovan. ''Dom Hans van der Laan: modern primitive'': Architectura & Natura Press, . The sequence was described by Ian Stewart (mathematician), Ian Stewart in his Scientific American column ''Mathematical Recreations'' in June 1996. He also writes about it in one of his books, "Math Hysteria: Fun Games With Mathematics". . ''The above definition is the one given by Ian Stewart and by MathWorld. Other sources may start the sequence at a different place, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedral Number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid (geometry), pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is, : Te_n = \sum_^n T_k = \sum_^n \frac = \sum_^n \left(\sum_^k i\right) The tetrahedral numbers are: :1, 4, 10, 20 (number), 20, 35 (number), 35, 56 (number), 56, 84 (number), 84, 120 (number), 120, 165 (number), 165, 220 (number), 220, ... Formula The formula for the th tetrahedral number is represented by the 3rd rising factorial of divided by the factorial of 3: :Te_n= \sum_^n T_k = \sum_^n \frac = \sum_^n \left(\sum_^k i\right)=\frac = \frac The tetrahedral numbers can also be represented as binomial coefficients: :Te_n=\binom. Tetrahedral numbers can therefore be found in the fourth position either from left or right in Pascal's triangle. Proofs of formula This proof uses the fact that the th triangular num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhex (mathematics)
In recreational mathematics, a polyhex is a polyform with a hexagon, regular hexagon (or 'hex' for short) as the base form, constructed by joining together 1 or more hexagons. Specific forms are named by their number of hexagons: ''monohex'', ''dihex'', ''trihex'', ''tetrahex'', etc. They were named by David Klarner who investigated them. Each individual polyhex tile and tessellation polyhexes and can be drawn on a regular hexagonal tiling. Construction rules The rules for joining hexagons together may vary. Generally, however, the following rules apply: #Two hexagons may be joined only along a common edge, and must share the entirety of that edge. #No two hexagons may overlap. #A polyhex must be connected. Configurations of disconnected basic polygons do not qualify as polyhexes. #The mirror image of an asymmetric polyhex is not considered a distinct polyhex (polyhex are "double sided"). Tessellation properties All of the polyhexes with fewer than five hexagons can form at le ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blum Integer
In mathematics, a natural number ''n'' is a Blum integer if is a semiprime for which ''p'' and ''q'' are distinct prime numbers congruent to 3 mod 4.Joe Hurd, Blum Integers (1997), retrieved 17 Jan, 2011 from http://www.gilith.com/research/talks/cambridge1997.pdf That is, ''p'' and ''q'' must be of the form , for some integer ''t''. Integers of this form are referred to as Blum primes. Goldwasser, S. and Bellare, M.br>"Lecture Notes on Cryptography". Summer course on cryptography, MIT, 1996-2001 This means that the factors of a Blum integer are Gaussian primes with no imaginary part. The first few Blum integers are : 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, 201, 209, 213, 217, 237, 249, 253, 301, 309, 321, 329, 341, 381, 393, 413, 417, 437, 453, 469, 473, 489, 497, ... The integers were named for computer scientist Manuel Blum. Properties Given a Blum integer, ''Q''''n'' the set of all quadratic residues modulo ''n'' and coprime to ''n'' and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pronic Number
A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular numbers; however, the term "rectangular number" has also been applied to the composite numbers. The first 60 pronic numbers are: : 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550, 2652, 2756, 2862, 2970, 3080, 3192, 3306, 3422, 3540, 3660... . Letting P_n denote the pronic number n(n+1), we have P_ = P_. Therefore, in discussing pronic numbers, we may assume that n\geq 0 without loss of generality, a convention that is adopted in the following sections. As figurate numbers The pronic numbers were studied as figurate nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens Function
In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: : M(x) = M(\lfloor x \rfloor). Less formally, M(x) is the count of square-free integers up to ''x'' that have an even number of prime factors, minus the count of those that have an odd number. The first 143 ''M''(''n'') values are The Mertens function slowly grows in positive and negative directions both on average and in peak value, oscillating in an apparently chaotic manner passing through zero when ''n'' has the values :2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427, 428, ... . Because the Möbius function only ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Prime (recreational Mathematics)
In recreational number theory, a minimal prime is a prime number for which there is no shorter subsequence of its digits in a given base that form a prime. In base 10 there are exactly 26 minimal primes: : 2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049 . For example, 409 is a minimal prime because there is no prime among the shorter subsequences of the digits: 4, 0, 9, 40, 49, 09. The subsequence does not have to consist of consecutive digits, so 109 is not a minimal prime (because 19 is prime). But it does have to be in the same order; so, for example, 991 is still a minimal prime even though a subset of the digits can form the shorter prime 19 by changing the order. Similarly, there are exactly 32 composite numbers which have no shorter composite subsequence: :4, 6, 8, 9, 10, 12, 15, 20, 21, 22, 25, 27, 30, 32, 33, 35, 50, 51, 52, 55, 57, 70, 72, 75, 77, 111, 117, 171, 371, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
