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It is an example of a 2-regular sequence. [ 2 ] Asymptotically , the value of the n {\displaystyle n} th sorting number fluctuates between approximately n log 2 n − n {\displaystyle n\log _{2}n-n} and n log 2 n − 0.915 n , {\displaystyle n\log _{2}n-0.915n,} depending on the ratio between n {\displaystyle n} and the nearest power of ...
A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...
An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
As a second example, for sequences in the real numbers, weak positivity (is for all ?) reduces to positivity of the sequence (because the answer must be negated, this is a Turing reduction). The Skolem-Mahler-Lech theorem would provide answers to some of these questions, except that its proof is non-constructive .
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The C POSIX library is a specification of a C standard library for POSIX systems. It was developed at the same time as the ANSI C standard. Some effort was made to make POSIX compatible with standard C; POSIX includes additional functions to those introduced in standard C. On the other hand, the 5 headers that were added to the C standard ...
if a ≤ b and b ≤ c then a ≤ c (transitivity) for all a and b, a ≤ b or b ≤ a . It is possible that both a ≤ b and b ≤ a; in this case either may come first in the sorted list. In a stable sort, the input order determines the sorted order in this case. Comparison sorts studied in the literature are "comparison-based". [1]