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A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
For =, the sum of the factorials of the digits is simply the number of digits in the base 2 representation since ! =! =. A natural number n {\displaystyle n} is a sociable factorion if it is a periodic point for SFD b {\displaystyle \operatorname {SFD} _{b}} , where SFD b k ( n ) = n {\displaystyle \operatorname {SFD} _{b}^{k}(n)=n} for a ...
Since ! is the product of the integers 1 through n, we obtain at least one factor of p in ! for each multiple of p in {,, …,}, of which there are ⌊ ⌋.Each multiple of contributes an additional factor of p, each multiple of contributes yet another factor of p, etc. Adding up the number of these factors gives the infinite sum for (!
The factorial number system is a mixed radix numeral system: the i-th digit from the right has base i, which means that the digit must be strictly less than i, and that (taking into account the bases of the less significant digits) its value is to be multiplied by (i − 1)! (its place value).
The concept of a decimal digit sum is closely related to, but not the same as, the digital root, which is the result of repeatedly applying the digit sum operation until the remaining value is only a single digit. The decimal digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value.
TI SR-50A, a 1975 calculator with a factorial key (third row, center right) The factorial function is a common feature in scientific calculators . [ 73 ] It is also included in scientific programming libraries such as the Python mathematical functions module [ 74 ] and the Boost C++ library . [ 75 ]
The solver can be built using Visual Studio, a makefile or using CMake and runs on Windows, FreeBSD, Linux, and macOS. The default input format for Z3 is SMTLIB2. It also has officially supported bindings for several programming languages, including C, C++, Python, .NET, Java, and OCaml. [5]
It was used in the world record calculations of 2.7 trillion digits of π in December 2009, [3] 10 trillion digits in October 2011, [4] [5] 22.4 trillion digits in November 2016, [6] 31.4 trillion digits in September 2018–January 2019, [7] 50 trillion digits on January 29, 2020, [8] 62.8 trillion digits on August 14, 2021, [9] 100 trillion ...