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Name First elements Short description OEIS Kolakoski sequence: 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ... The n th term describes the length of the n th run : A000002: Euler's ...
For example, 1 + 2 ≡ 3 (mod 6) corresponds to z 1 · z 2 = z 3, and 2 + 5 ≡ 1 (mod 6) corresponds to z 2 · z 5 = z 7 = z 1, and so on. Any element generates its own cyclic subgroup, such as z 2 = { e , z 2 , z 4 } of order 3, isomorphic to C 3 and Z /3 Z ; and z 5 = { e , z 5 , z 10 = z 4 , z 15 = z 3 , z 20 = z 2 , z 25 = z } = G , so ...
Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary : The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal : Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc. Various notations have been used to represent hyperoperations.
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
In mathematics, a well-defined expression or unambiguous expression is an expression whose definition assigns it a unique interpretation or value. Otherwise, the expression is said to be not well defined, ill defined or ambiguous. [1]
Using all numbers and all letters except I and O; the smallest base where 1 / 2 terminates and all of 1 / 2 to 1 / 18 have periods of 4 or shorter. 35: Covers the ten decimal digits and all letters of the English alphabet, apart from not distinguishing 0 from O. 36: Hexatrigesimal [57] [58]
The unary numeral system is the simplest numeral system to represent natural numbers: [1] to represent a number N, a symbol representing 1 is repeated N times. [2]In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol.