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Mian–Chowla Sequence
In mathematics, the Mian–Chowla sequence is an integer sequence defined recursion, recursively in the following way. The sequence starts with :a_1 = 1. Then for n>1, a_n is the smallest integer such that every pairwise sum :a_i + a_j is distinct, for all i and j less than or equal to n. Properties Initially, with a_1, there is only one pairwise sum, 1 + 1 = 2. The next term in the sequence, a_2, is 2 since the pairwise sums then are 2, 3 and 4, i.e., they are distinct. Then, a_3 can't be 3 because there would be the non-distinct pairwise sums 1 + 3 = 2 + 2 = 4. We find then that a_3 = 4, with the pairwise sums being 2, 3, 4, 5, 6 and 8. The sequence thus begins :1 (number), 1, 2 (number), 2, 4 (number), 4, 8 (number), 8, 13 (number), 13, 21 (number), 21, 31 (number), 31, 45 (number), 45, 66 (number), 66, 81 (number), 81, 97 (number), 97, 123 (number), 123, 148 (number), 148, 182 (number), 182, 204 (number), 204,252 (number), 252, 290 (number), 290, 361, 401, 475, ... . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
66 (number)
66 (sixty-six) is the natural number following 65 and preceding 67. Usages of this number include: In mathematics 66 is: *a sphenic number. *a triangular number. *a hexagonal number. *a semi-meandric number. *a semiperfect number, being a multiple of a perfect number. *an Erdős–Woods number, since it is possible to find sequences of 66 consecutive integers such that each inner member shares a factor with either the first or the last member. *palindromic and a repdigit in bases 10 (6610), 21 (3321) and 32 (2232) In science Astronomy *Messier object Spiral Galaxy M66, a magnitude 10.0 galaxy in the constellation Leo. *The New General Catalogue object NGC 66, a peculiar barred spiral galaxy in the constellation Cetus. * 66 Maja, a carbonaceous background asteroid from the central regions of the asteroid belt. Physics *The atomic number of dysprosium, a lanthanide. In computing 66 (more specifically 66.667) megahertz (MHz) is a common divisor for the front side bus (F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
290 (number)
290 (two hundred ndninety) is the natural number following 289 and preceding 291. In mathematics The product of three primes, 290 is a sphenic number, and the sum of four consecutive primes (67 + 71 + 73 + 79). The sum of the squares of the divisors of 17 is 290. Not only is it a nontotient and a noncototient, it is also an untouchable number. 290 is the 16th member of the Mian–Chowla sequence; it can not be obtained as the sum of any two previous terms in the sequence. See also the Bhargava–Hanke 290 theorem. In other fields *"290" was the shipyard number of the ''CSS Alabama'' See also the year 290. Integers from 291 to 299 291 291 = 3·97, a semiprime, floor(3^14/2^14) . 292 292 = 22·73, noncototient, untouchable number. The continued fraction representation of \pi is ; 7, 15, 1, 292, 1, 1, 1, 2... the convergent obtained by truncating before the surprisingly large term 292 yields the excellent rational approximation 355/113 to \pi, repdigit in base 8 (444). 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
252 (number)
252 (two hundred ndfifty-two) is the natural number following 251 and preceding 253. In mathematics 252 is: *the central binomial coefficient \tbinom, the largest one divisible by all coefficients in the previous line *\tau(3), where \tau is the Ramanujan tau function. *\sigma_3(6), where \sigma_3 is the function that sums the cubes of the divisors of its argument: :1^3+2^3+3^3+6^3=(1^3+2^3)(1^3+3^3)=252. *a practical number, *a refactorable number, *a hexagonal pyramidal number. *a member of the Mian-Chowla sequence. There are 252 points on the surface of a cuboctahedron of radius five in the face-centered cubic lattice, 252 ways of writing the number 4 as a sum of six squares of integers, 252 ways of choosing four squares from a 4×4 chessboard up to reflections and rotations, and 252 ways of placing three pieces on a Connect Four Connect Four (also known as Connect 4, Four Up, Plot Four, Find Four, Captain's Mistress, Four in a Row, Drop Four, and Gravitrips in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
204 (number)
204 (two hundred ndfour) is the natural number following 203 and preceding 205. In mathematics 204 is a refactorable number. 204 is a square pyramidal number: 204 balls may be stacked in a pyramid whose base is an 8 × 8 square. Its square, 2042 = 41616, is the fourth square triangular number. As a figurate number, 204 is also a nonagonal number and a truncated triangular pyramid number. 204 is a member of the Mian-Chowla sequence. There are exactly 204 irreducible quintic polynomials over a four-element field, exactly 204 ways to place three non-attacking chess queens on a 5 × 5 board, exactly 204 squares of an infinite chess move that are eight knight's moves from the center, exactly 204 strings of length 11 over a three-letter alphabet with no consecutively-repeated substring, and exactly 204 ways of immersing an oriented circle into the oriented plane so that it has four double points. Both 204 and its square are sums of a pair of twin p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
182 (number)
182 (one hundred ndeighty-two) is the natural number following 181 and preceding 183. In mathematics * 182 is an even number * 182 is a composite number, as it is a positive integer with a positive divisor other than one or itself * 182 is a deficient number, as the sum of its proper divisors, 154, is less than 182 * 182 is a member of the Mian–Chowla sequence: 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182 * 182 is a nontotient number, as there is no integer with exactly 182 coprimes below it * 182 is an odious number * 182 is a pronic number, oblong number or heteromecic number, a number which is the product of two consecutive integers ( 13 × 14) * 182 is a repdigit in the D'ni numeral system ( 77), and in base 9 ( 222) * 182 is a sphenic number, the product of three prime factors * 182 is a square-free number * 182 is an Ulam number * Divisors of 182: 1, 2, 7, 13, 14, 26, 91, 182 In astronomy * 182 Elsa is a S-type main belt asteroid * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
148 (number)
148 (one hundred ndforty-eight) is the natural number following 147 and before 149. In mathematics 148 is the second number to be both a heptagonal number and a centered heptagonal number (the first is 1). It is the twelfth member of the Mian–Chowla sequence, the lexicographically smallest sequence of distinct positive integers with distinct pairwise sums. There are 148 perfect graphs with six vertices, and 148 ways of partitioning four people into subsets, ordering the subsets, and selecting a leader for each subset. In other fields In the Book of Nehemiah 7:44 there are 148 singers, sons of Asaph, at the census of men of Israel upon return from exile. This differs from Ezra 2:41, where the number is given as 128. Dunbar's number is a theoretical cognitive limit to the number of people with whom one can maintain stable interpersonal relationships. Dunbar predicted a "mean group size" of 148, but this is commonly rounded to 150. See also * The year AD 148 or 148 BC _ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
123 (number)
123 (one hundred ndtwenty-three) is the natural number following 122 and preceding 124. In mathematics *123 is a Lucas number. It is the eleventh member of the Mian-Chowla sequence. *Along with 6, 123 is one of only two positive integers that is simultaneously two more than a perfect square and two less than a perfect cube (123 = 112 + 2 = 53 - 2). In religion The Book of Numbers says that Aaron died at the age of 123. In telephony *The emergency telephone number in Colombia *The telephone number of the speaking clock for the correct time in the United Kingdom *The electricity ( PLN) emergency telephone number in Indonesia *The medical emergency telephone number in Egypt *The Notation for national and international telephone numbers Recommendation ITU-T Recommendation E.123 defines a standard way to write telephone numbers, e-mail addresses, and web addresses In other fields 123 is also: * ''123'' (film), a 2002 Indian film *123 (interbank network), shared cash network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
97 (number)
97 (ninety-seven) is the natural number following 96 and preceding 98. It is a prime number and the only prime in the nineties. In mathematics 97 is: * the 25th prime number (the largest two-digit prime number in base 10), following 89 and preceding 101. * a Proth prime and a Pierpont prime as it is 3 × 25 + 1. * the eleventh member of the Mian–Chowla sequence. * a self number in base 10, since there is no integer that added to its own digits, adds up to 97. * the smallest odd prime that is not a cluster prime. * the highest two-digit number where the sum of its digits is a square. * the number of primes <= 29. * The numbers 97, 907, 9007, 90007 and 900007 are all primes, and they are all s. However, 9000007 (read as ''nine million seven'') is |
81 (number)
81 (eighty-one) is the natural number following 80 and preceding 82. In mathematics 81 is: * the square of 9 and the fourth power of 3. * a perfect totient number like all powers of three. * a heptagonal number. * a centered octagonal number. * a tribonacci number. * an open meandric number. * the ninth member of the Mian-Chowla sequence. * a palindromic number in bases 8 (1218) and 26 (3326). * a Harshad number in bases 2, 3, 4, 7, 9, 10 and 13. * one of three non-trivial numbers (the other two are 1458 and 1729) which, when its digits (in decimal) are added together, produces a sum which, when multiplied by its reversed self, yields the original number: : 8 + 1 = 9 : 9 × 9 = 81 (although this case is somewhat degenerate, as the sum has only a single digit). The inverse of 81 is 0. recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base ''b'', :\frac = 0.\overline, omitting only the digit ''b'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
45 (number)
45 (forty-five) is the natural number following 44 (number), 44 and followed by 46 (number), 46. In mathematics Forty-five is the smallest Parity (mathematics), odd number that has more divisors than n+1, and that has a larger sum of divisors than n+1. It is the sixth positive integer with a prime factorization of the form p^q, with and being Prime number, prime. Forty-five is the summation, sum of all single-digit decimal digits: 0+1+2+3+4+5+6+7+8+9=45. It is, equivalently, the ninth triangle number. Forty-five is also the fourth hexagonal number and the second polygonal number, hexadecagonal number, or 16-gonal number. It is also the second smallest triangle number (after 1 and 10) that can be written as the sum of two squares. Since the greatest prime factor of 45^+1=2026 is 1,013, which is much more than 45 twice, 45 is a Størmer number. In decimal, 45 is a Kaprekar number and a Harshad number. Forty-five is a oeis:A001003, little Schroeder number; the next suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Sequence
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified ''explicitly'' by giving a formula for its ''n''th term, or ''implicitly'' by giving a relationship between its terms. For example, the sequence 0, 1, 1, 2, 3, 5, 8, 13, ... (the Fibonacci sequence) is formed by starting with 0 and 1 and then adding any two consecutive terms to obtain the next one: an implicit description. The sequence 0, 3, 8, 15, ... is formed according to the formula ''n''2 − 1 for the ''n''th term: an explicit definition. Alternatively, an integer sequence may be defined by a property which members of the sequence possess and other integers do not possess. For example, we can determine whether a given integer is a perfect number, even though we do not have a formula for the ''n''th perfect number. Examples Integer sequences that have their own name include: *Abundant numbers *Baum–Sweet sequence *Bell numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
