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4200
4000 (four thousand) is the natural number following 3999 and preceding 4001. It is a decagonal number. Selected numbers in the range 4001–4999 4001 to 4099 * 4005 – triangular number * 4007 – safe prime * 4010 – magic constant of ''n'' × ''n'' normal magic square and ''n''-queens problem for ''n'' = 20 * 4013 – balanced prime * 4019 – Sophie Germain prime * 4021 – prime of the form 2p-1 * 4027 – super-prime * 4028 – sum of the first 45 primes * 4030 – third weird number * 4031 – sum of the cubes of the first six primes * 4032 – pronic number * 4033 – sixth super-Poulet number; strong pseudoprime in base 2 * 4057 – prime of the form 2p-1 * 4060 – tetrahedral number * 4073 – Sophie Germain prime * 4079 – safe prime * 4091 – super-prime * 4095 – triangular number and odd abundant number; number of divisors in the sum of the fifth and largest known unitary perfect number, largest Ramanujan–Nagell number of the form 2^ - 1 * 4096 = 642 = ... [...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] |
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] |
Fibonacci Number
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Heptagonal Number
A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for ''n'' is given by the formula :\over2. The first few centered heptagonal numbers are 1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953 Centered heptagonal prime A centered heptagonal prime is a centered heptagonal number that is prime. The first few centered heptagonal primes are :43, 71, 197, 463, 547, 953, 1471, 1933, 2647, 2843, 3697, ... The centered heptagonal twin prime A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ... numbers are :43, 71, 197, 463, 1933, 5741, 8233, 9283, 11173, 14561, 34651, ... See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base-12
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared (144), "1,000" means twelve cubed (1,728), and "0.1" means a twelfth (0.08333...). Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses and , as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , and finally 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: (a turned 2) for ten (dek, pronounced dɛk) and (a turned 3) for eleven (el, pronounced ɛl). The number twelve, a superior highly composite number, is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Number
A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the six-digit number 142857, whose first six integer multiples are :142857 × 1 = 142857 :142857 × 2 = 285714 :142857 × 3 = 428571 :142857 × 4 = 571428 :142857 × 5 = 714285 :142857 × 6 = 857142 Details To qualify as a cyclic number, it is required that consecutive multiples be cyclic permutations. Thus, the number 076923 would not be considered a cyclic number, because even though all cyclic permutations are multiples, they are not consecutive integer multiples: :076923 × 1 = 076923 :076923 × 3 = 230769 :076923 × 4 = 307692 :076923 × 9 = 692307 :076923 × 10 = 769230 :076923 × 12 = 923076 The following trivial cases are typically excluded: #single digits, e.g.: 5 #repeated digits, e.g.: 555 #repeated cyclic numbers, e.g.: 142857142857 If leading zeros are no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Square Number
In elementary number theory, a centered square number is a Centered polygonal number, centered figurate number that gives the number of dots in a Square (geometry), square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a given Taxicab geometry, city block distance of the center dot on a regular square lattice. While centered square numbers, like figurate numbers in general, have few if any direct practical applications, they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties. The figures for the first four centered square numbers are shown below: : Each centered square number is the sum of successive squares. Example: as shown in the following figure of Floyd's triangle, 25 is a centered square number, and is the sum of the square 16 (yellow rhombus formed by shearing a square) and of the next smaller sq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy, they are named after Eric Temple Bell, who wrote about them in the 1930s. The Bell numbers are denoted B_n, where n is an integer greater than or equal to zero. Starting with B_0 = B_1 = 1, the first few Bell numbers are :1, 1, 2, 5, 15, 52, 203, 877, 4140, \dots . The Bell number B_n counts the different ways to partition a set that has exactly n elements, or equivalently, the equivalence relations on it. B_n also counts the different rhyme schemes for n -line poems. As well as appearing in counting problems, these numbers have a different interpretation, as moments of probability distributions. In particular, B_n is the n -th moment of a Poisson distribution with mean 1. Counting Set partitions In general, B_n is the number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
4104 (number)
4104 (four thousand one hundred ndfour) is the natural number following 4103 and preceding 4105. It is the second positive integer which can be expressed as the sum of two positive cubes in two different ways. The first such number, 1729, is called the " Ramanujan–Hardy number". 4104 is the sum of 4096 + 8 (that is, 163 + 23), and also the sum of 3375 + 729 (that is, 153 + 93). See also * Taxicab number * 1729 Events January–March * January 8 – Frederick, the eldest son of King George II of Great Britain is made Prince of Wales at the age of 21, a few months after he comes to Britain for the first time after growing up in Hanover ... External links MathWorld: Hardy–Ramanujan Number {{DEFAULTSORT:4104 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superperfect Number
In number theory, a superperfect number is a positive integer that satisfies :\sigma^2(n)=\sigma(\sigma(n))=2n\, , where is the sum-of-divisors function. Superperfect numbers are not a generalization of perfect numbers but have a common generalization. The term was coined by D. Suryanarayana (1969). The first few superperfect numbers are: : 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, ... . To illustrate: it can be seen that 16 is a superperfect number as , and , thus . If is an '' even'' superperfect number, then must be a power of 2, , such that is a Mersenne prime. It is not known whether there are any odd superperfect numbers. An odd superperfect number would have to be a square number In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals ... such that either or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Of Two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^n(1). In the Hardy hierarchy, is exactly equal to H_(1). Powers of two with Sign (mathematics)#Terminology for signs, non-negative exponents are integers: , , and is two multiplication, multiplied by itself times. The first ten powers of 2 for non-negative values of are: :1, 2, 4, 8, 16 (number), 16, 32 (number), 32, 64 (number), 64, 128 (number), 128, 256 (number), 256, 512 (number), 512, ... By comparison, powers of two with negative exponents are fractions: for positive integer , is one half multiplied by itself times. Thus the first few negative powers of 2 are , , , , etc. Sometimes these are called ''inverse powers of two'' because each is the multiplicative inverse of a positive power of two. Base of the binary numeral sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
