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Lazy Caterer's Sequence
The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a Disk (mathematics), disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point inside the circle, but up to seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, ''see'' arrangement of hyperplanes. The analogue of this integer sequence, sequence in three dimensions is the cake numbers. Formula and sequence The maximum number ''p'' of pieces that can be created with a given number of cuts (where ) is given by the formula :p = \frac. Using binomial coefficients, the formula can be expressed as :p = 1 + \dbinom = \dbinom+\dbinom+\dbinom. Simply put, each number equals a triang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
29 (number)
29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number. 29 is the number of days February has on a leap year. Mathematics 29 is the tenth prime number. Integer properties 29 is the fifth primorial prime, like its twin prime 31. 29 is the smallest positive whole number that cannot be made from the numbers \, using each digit exactly once and using only addition, subtraction, multiplication, and division. None of the first twenty-nine natural numbers have more than two different prime factors (in other words, this is the longest such consecutive sequence; the first sphenic number or triprime, 30 is the product of the first three primes 2, 3, and 5). 29 is also, * the sum of three consecutive squares, 22 + 32 + 42. * the sixth Sophie Germain prime. * a Lucas prime, a Pell prime, and a tetranacci number. * an Eisenstein prime with no imaginary part and real part of the form 3n − 1. * a Markov number, appearing in the solution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
211 (number)
211 (two hundred ndeleven) is the natural number following 210 and preceding 212. It is also a prime number. In mathematics * 211 is the sum of three consecutive primes (67+71+73), a Chen prime, a centered decagonal prime, and a self prime. * 211 is the smallest prime separated by 12 from the nearest primes (199 and 223). It is thus a balanced prime and an '' isolated prime''. *211 is a repdigit in tetradecimal (111). * 211 is the 47th prime number and therefore it is a super-prime. In other fields 211 is also a nickname for Steel Reserve, a malt liquor alcoholic beverage. 211 is also SMTP The Simple Mail Transfer Protocol (SMTP) is an Internet standard communication protocol for electronic mail transmission. Mail servers and other message transfer agents use SMTP to send and receive mail messages. User-level email clients typi ... status code for system status. References Integers {{num-stub ca:Nombre 210#Nombres del 211 al 219 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
191 (number)
191 (one hundred ndninety-one) is the natural number following 190 and preceding 192. In mathematics 191 is a prime number, part of a prime quadruplet of four primes: 191, 193, 197, and 199. Because doubling and adding one produces another prime number (383), 191 is a Sophie Germain prime. It is the smallest prime that is not a full repetend prime in ''any'' base from 2 to 10; in fact, the smallest base for which 191 is a full period prime is base 19 There are many different numeral systems, that is, writing systems for expressing numbers. By culture / time period "A ''base'' is a natural number B whose ''powers'' (B multiplied by itself some number of times) are specially designated wit ....Wolfram MathWorldPrimitive Root/ref> See also * 191 (other) References Integers {{num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
172 (number)
172 (one hundred ndseventy-two) is the natural number following 171 and preceding 173. In mathematics 172 is a part of a near-miss for being a counterexample to Fermat's last theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive number, positive integers , , and satisfy the equation for any integer value of greater than . The cases ..., as 1353 + 1383 = 1723 − 1. This is only the third near-miss of this form, two cubes adding to one less than a third cube. It is also a "thickened cube number", half an odd cube (73 = 343) rounded up to the next integer. See also * 172 (other) References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
154 (number)
154 (one hundred ndfifty-four) is the natural number following 153 and preceding 155. In mathematics 154 is a nonagonal number. Its factorization makes 154 a sphenic number. There is no integer with exactly 154 coprimes below it, making 154 a noncototient, nor is there, in base 10, any integer that added up to its own digits yields 154, making 154 a self number 154 is the sum of the first six factorials, if one starts with 0! and assumes that 0!=1. With just 17 cuts, a pancake can be cut up into 154 pieces ( Lazy caterer's sequence). The distinct prime factors of 154 add up to 20, and so do the ones of 153, hence the two form a Ruth-Aaron pair. 154! + 1 is a factorial prime A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are : : 2 (0! + 1 or 1! + 1) .... References * Wells, D. '' The Penguin Diction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
137 (number)
137 (one hundred [and] thirty-seven) is the natural number following 136 (number), 136 and preceding 138 (number), 138. Mathematics 137 is: * the 33rd prime number; the next is 139 (number), 139, with which it comprises a twin prime, and thus 137 is a Chen prime. * an Eisenstein prime with no imaginary part and a real part of the form 3n - 1. * the fourth Stern prime. * a Pythagorean prime: a prime number of the form 4n+1, where n=34 (137=4\times 34+1) or the sum of two squares 11^+4^ = (121+16). * a combination of three terms 4^+3^-2^ = (64+81-8), cube of 4 + Triangular number T4+T2 on each cube face (along 3 axes) - peaks (single 6th peak as free link) * a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes. * a strictly non-palindromic number and a primeval number. * a factor of 10001 (the other being 73 (number), 73) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
121 (number)
121 (one hundred ndtwenty-one) is the natural number following 120 and preceding 122. In mathematics ''One hundred ndtwenty-one'' is * a square (11 times 11) * the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form 1 + p + p^2 + p^3 + p^4, where ''p'' is prime (3, in this case). * the sum of three consecutive prime numbers (37 + 41 + 43). * As 5! + 1 = 121, it provides a solution to Brocard's problem. There are only two other squares known to be of the form n! + 1. Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form x^-4 (with being 2 and 5, respectively).Wells, D., '' The Penguin Dictionary of Curious and Interesting Numbers'', London: Penguin Group. (1987): 136 * It is also a star number, a centered tetrahedral number, and a centered octagonal number. * In decimal, it is a Smith number since its digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
106 (number)
106 (one hundred ndsix) is the natural number following 105 and preceding 107 107 may refer to: *107 (number), the number *AD 107, a year in the 2nd century AD *107 BC, a year in the 2nd century BC *107 (New Jersey bus) *107 Camilla, a main-belt asteroid *Peugeot 107, a city car See also *10/7 (other) *Bohrium, .... In mathematics 106 is a centered pentagonal number, a centered heptagonal number, and a regular 19-gonal number. There are 106 mathematical trees with ten vertices. See also * 106 (other) References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
92 (number)
92 (ninety-two) is the natural number following 91 and preceding 93. In mathematics Form 92 is a composite number of the general form ''p''2''q'', where ''q'' is a higher prime ( 23). It is the tenth of this form and the eighth of the form 22''q''. Properties There are 92 "atomic elements" in John Conway's look-and-say sequence, corresponding to the 92 non-transuranic elements in the chemist's periodic table. Solids The most faces or vertices an Archimedean or Catalan solid can have is 92: the snub dodecahedron has 92 faces while its dual polyhedron, the pentagonal hexecontahedron, has 92 vertices. On the other hand, as a simple polyhedron, the final stellation of the icosahedron has 92 vertices. There are 92 Johnson solids. Abstract algebra 92 is the total number of objects that are permuted by the series of five finite, simple Mathieu groups \mathbb M_ (collectively), as defined by permutations based on elements n \in \. Half of 92 is 46 (the largest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
79 (number)
79 (seventy-nine) is the natural number following 78 (number), 78 and preceding 80 (number), 80. In mathematics 79 is: * An even and odd numbers, odd number. * The smallest number that can not be represented as a sum of fewer than 19 fourth powers. * The 22nd prime number (between and ) * An isolated prime without a twin prime, as 77 and 81 are composite. * The smallest prime number ''p'' for which the real quadratic field Q[] has Ideal class group, class number greater than 1 (namely 3). * A cousin prime with 83. * An emirp in base 10, because the reverse of 79, 97 (number), 97, is also a prime. * A Fortunate prime. * A circular prime. * A prime number that is also a Gaussian prime (since it is of the form ). * A happy prime. * A Higgs prime. * A lucky prime. * A permutable prime, with 97 (number), ninety-seven. * A Pillai prime, because 23Factorial, ! + 1 is divisible by 79, but 79 is not one more than a Multiple (mathematics), multiple of 23 (number), 23. * A regular prime. * A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
67 (number)
67 (sixty-seven) is the natural number following 66 (number), 66 and preceding 68 (number), 68. It is an Parity (mathematics), odd and prime number. In mathematics 67 is: *the 19th prime number (the next is 71 (number), 71). * a Chen prime. *an irregular prime. *a lucky prime. *the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). *a Heegner number. *a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. *palindromic in quinary (2325) and senary (1516). *a super-prime. (19 is prime) *an Twin prime#Isolated prime, isolated prime. (65 and 69 are not prime) *a sexy prime with 61 and 73 References External links Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
