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Here is a complete program defining and using the traditional recursive function to calculate a factorial. % Accepts a number and calculates its factorial function factorial (n: int) : real if n = 0 then result 1 else result n * factorial (n - 1) end if end factorial var n: int loop put "Please input an integer: "..
In number theory, the Kempner function [1] is defined for a given positive integer to be the smallest number such that divides the factorial!. For example, the number 8 {\displaystyle 8} does not divide 1 ! {\displaystyle 1!} , 2 ! {\displaystyle 2!} , or 3 ! {\displaystyle 3!} , but does divide 4 ! {\displaystyle 4!} , so S ( 8 ) = 4 ...
Python is a high-level, general-purpose programming language that is popular in artificial intelligence. [1] It has a simple, flexible and easily readable syntax. [2] Its popularity results in a vast ecosystem of libraries, including for deep learning, such as PyTorch, TensorFlow, Keras, Google JAX.
JAX is a machine learning framework for transforming numerical functions developed by Google with some contributions from Nvidia. [2] [3] [4] It is described as bringing together a modified version of autograd (automatic obtaining of the gradient function through differentiation of a function) and OpenXLA's XLA (Accelerated Linear Algebra).
Z3 was developed in the Research in Software Engineering (RiSE) group at Microsoft Research Redmond and is targeted at solving problems that arise in software verification and program analysis.
(resulting in 24 factorial primes - the prime 2 is repeated) No other factorial primes are known as of December 2024 [update] . When both n ! + 1 and n ! − 1 are composite , there must be at least 2 n + 1 consecutive composite numbers around n !, since besides n ! ± 1 and n ! itself, also, each number of form n ! ± k is divisible by k for 2 ...
The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2] For n > 0 , the subfactorial !n equals the nearest integer to n!/e, where n!
Generative artificial intelligence (generative AI, GenAI, [1] or GAI) is a subset of artificial intelligence that uses generative models to produce text, images, videos, or other forms of data. [ 2 ] [ 3 ] [ 4 ] These models learn the underlying patterns and structures of their training data and use them to produce new data [ 5 ] [ 6 ] based on ...