|
Self Number
In number theory, a self number or Devlali number in a given number base b is a natural number that cannot be written as the sum of any other natural number n and the individual digits of n. 20 is a self number (in base 10), because no such combination can be found (all n 1 F_b : \mathbb \rightarrow \mathbb to be the following: :F_(n) = n + \sum_^ d_i. where k = \lfloor \log_ \rfloor + 1 is the number of digits in the number in base b, and :d_i = \frac is the value of each digit of the number. A natural number n is a b-self number if the preimage of n for F_b is the empty set. In general, for even bases, all odd numbers below the base number are self numbers, since any number below such an odd number would have to also be a 1-digit number which when added to its digit would result in an even number. For odd bases, all odd numbers are self numbers.Sándor & Crstici (2004) p.384 The set of self numbers in a given base b is infinite and has a positive asymptotic density: when b i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
5 (number)
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has attained significance throughout history in part because typical humans have five digits on each hand. In mathematics 5 is the third smallest prime number, and the second super-prime. It is the first safe prime, the first good prime, the first balanced prime, and the first of three known Wilson primes. Five is the second Fermat prime and the third Mersenne prime exponent, as well as the third Catalan number, and the third Sophie Germain prime. Notably, 5 is equal to the sum of the ''only'' consecutive primes, 2 + 3, and is the only number that is part of more than one pair of twin primes, ( 3, 5) and (5, 7). It is also a sexy prime with the fifth prime number and first prime repunit, 11. Five is the third factorial prime, an alternating factorial, and an Eisenstein prime with no imaginary part and real part of the for ... [...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). * 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 add up to the same value as its factorization (which uses the same digits) and as a consequence of that it is a Frie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
110 (number)
110 (one hundred ndten) is the natural number following 109 and preceding 111. In mathematics 110 is a sphenic number and a pronic number. Following the prime quadruplet (101, 103, 107, 109), at 110, the Mertens function reaches a low of −5. 110 is the sum of three consecutive squares, 110 = 5^2 + 6^2 + 7^2. RSA-110 is one of the RSA numbers, large semiprimes that are part of the RSA Factoring Challenge. In base 10, the number 110 is a Harshad number and a self number. In science * The atomic number of darmstadtium. In religion * According to the Bible, the figures Joseph and Joshua both died at the age of 110. In sports Olympic male track and field athletics run 110 metre hurdles. (Female athletes run the 100 metre hurdles instead.) The International 110, or the 110, is a one-design racing sailboat designed in 1939 by C. Raymond Hunt. In other fields 110 is also: * The year AD 110 or 110 BC * A common name for mains electricity in North America, despite the nomina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
108 (number)
108 (one hundred ndeight) is the natural number following 107 and preceding 109. In mathematics 108 is: *an abundant number. *a semiperfect number. *a tetranacci number. *the hyperfactorial of 3 since it is of the form 1^1 \cdot 2^2 \cdot 3^3. *divisible by the value of its φ function, which is 36. *divisible by the total number of its divisors (12), hence it is a refactorable number. *the angle in degrees of the interior angles of a regular pentagon in Euclidean space. *palindromic in bases 11 (9911), 17 (6617), 26 (4426), 35 (3335) and 53 (2253) *a Harshad number in bases 2, 3, 4, 6, 7, 9, 10, 11, 12, 13 and 16 *a self number. *an Achilles number because it is a powerful number but not a perfect power. *nine dozen There are 108 free polyominoes of order 7. The equation 2\sin\left(\frac\right) = \phi results in the golden ratio. This could be restated as saying that the " chord" of 108 degrees is \phi , the golden ratio. Religion and the arts The number 108 is ... [...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 |
86 (number)
86 (eighty-six) is the natural number following 85 (number), 85 and preceding 87 (number), 87. In mathematics 86 is: * nontotient and a noncototient. * the 25th distinct semiprime and the 13th of the form (2×q). * an Erdős–Woods number, since it is possible to find sequences of 86 consecutive integers such that each inner member shares a factor with either the first or the last member. * a happy number and a self number in base 10. It appears in the Padovan sequence, preceded by the terms 37, 49, 65 (it is the sum of the first two of these). It is conjectured that 86 is the largest n for which the decimal expansion of 2n contains no 0. 86 = (8 × 6 = 48) + (4 × 8 = 32) + (3 × 2 = 6). That is, 86 is equal to the sum of the numbers formed in calculating its Persistence of a number, multiplicative persistence. In science * 86 is the atomic number of radon. * There are 86 metals on the modern periodic table. In other fields *In American English, and particularly in the food ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
75 (number)
75 (seventy-five) is the natural number following 74 and preceding 76. __TOC__ In mathematics 75 is a self number because there is no integer that added up to its own digits adds up to 75. It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number. It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75... 75 is the count of the number of weak orderings on a set of four items. Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra. In other fields Seventy-five is: *The atomic number of rhenium *The age limit for Canadian senators [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
64 (number)
64 (sixty-four) is the natural number following 63 and preceding 65. In mathematics Sixty-four is the square of 8, the cube of 4, and the sixth power of 2. It is the smallest number with exactly seven divisors. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number. 64 is also the first whole number (greater than 1) that is both a perfect square and a perfect cube. Since it is possible to find sequences of 64 consecutive integers such that each inner member shares a factor with either the first or the last member, 64 is an ErdÅ‘s–Woods number. In base 10, no integer added up to its own digits yields 64, hence it is a self number. 64 is a superperfect number—a number such that σ(σ(''n'')) = 2''n''. 64 is the index of Graham's number in the rapidly growing sequence 3 ↑↑↑â ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
53 (number)
53 (fifty-three) is the natural number following 52 and preceding 54. It is the 16th prime number. In mathematics *Fifty-three is the 16th prime number. It is also an Eisenstein prime, an isolated prime, a balanced prime and a Sophie Germain prime. *The sum of the first 53 primes is 5830, which is divisible by 53, a property shared by only a few other numbers. *In hexadecimal, 53 is 35, that is, the same characters used in the decimal representation, but reversed. Four additional multiples of 53 share this property: 371 = , 5141 = , 99,481 = , and 8,520,280 = 0. Apart from the trivial case of single-digit decimals, no other number has this property. *53 cannot be expressed as the sum of any integer and its decimal digits, making 53 a self number. *53 is the smallest prime number that does not divide the order of any sporadic group. In science *The atomic number of iodine Astronomy *Messier object M53, a magnitude 8.5 globular cluster in the constellation Coma Berenices *The N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
42 (number)
42 (forty-two) is the natural number that follows 41 (number), 41 and precedes 43 (number), 43. Mathematics Forty-two (42) is a pronic number and an abundant number; its prime factorization (2\times 3\times 7) makes it the second sphenic number and also the second of the form (2\times 3\times r). Additional properties of the number 42 include: * It is the number of isomorphism classes of all simple and oriented directed graphs on 4 vertices. In other words, it is the number of all possible outcomes (up to isomorphism) of a tournament consisting of 4 teams where the game between any pair of teams results in three possible outcomes: the first team wins, the second team wins, or there is a draw. The group stage of the FIFA World cup is a good example. * It is the third primary pseudoperfect number. * It is a Catalan number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered bina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
31 (number)
31 (thirty-one) is the natural number following thirty, 30 and preceding 32 (number), 32. It is a prime number. In mathematics 31 is the 11th prime number. It is a superprime and a Self number#Self primes, self prime (after 3, 5, and 7), as no integer added up to its base 10 digits results in 31. It is a lucky prime and a happy number; two properties it shares with 13 (number), 13, which is its dual emirp and permutable prime. 31 is also a primorial prime, like its twin prime, 29 (number), 29. 31 is the number of regular polygons with an odd number of sides that are known to be constructible polygon, constructible with compass and straightedge, from combinations of known Fermat primes of the form 22''n'' + 1. 31 is the third Mersenne prime of the form 2''n'' − 1. It is also the eighth Mersenne prime exponent, specifically for the number 2,147,483,647, which is the maximum positive value for a 32-bit Integer (computer science), signed binary integer in computing. After 3, it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_of_Tulasi_wood_with_108_beads_-_20040101-02.jpg "Click for more on -> 108 (number)")
