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In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [1]In his 1947 paper, [2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations.
Order of operations. In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and ... (which begins 1, 8, 27, ... Sequence space; Operations ...
In 1953, Leo Moser proved that there is a single infinite Salem–Spencer sequence achieving the same asymptotic density on every prefix as Behrend's construction. [1] By considering the convex hull of points inside a sphere, rather than the set of points on a sphere, it is possible to improve the construction by a factor of log n ...
Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...
In mathematics, the hyperoperation sequence [nb 1] is an infinite sequence of arithmetic operations (called hyperoperations in this context) [1] [11] [13] that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3).
In 2017, it was proven [14] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...
Note that the process of going from the sequence =(10→n) to the sequence =(10→10→n) is very similar to going from the latter to the sequence () =(10→10→10→n): it is the general process of adding an element 10 to the chain in the chain notation; this process can be repeated again (see also the previous section).