Search results
Results from the WOW.Com Content Network
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 ...
The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS). In this article, a factorial number representation will be flagged by a subscript "!". In addition, some examples will have digits delimited by a colon. For example, 3:4:1:0:1:0! stands for
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 5×4×3×2×1 = 120. By convention, the value of 0! is defined as 1. This classical factorial function appears prominently in many theorems in number theory. The following are a few of these theorems. [1]
[39] [40] The factorial number system is a mixed radix notation for numbers in which the place values of each digit are factorials. [ 41 ] Factorials are used extensively in probability theory , for instance in the Poisson distribution [ 42 ] and in the probabilities of random permutations . [ 43 ]
The q-analog of n, also known as the q-bracket or q-number of n, is defined to be [] =. From this one can define the q -analog of the factorial , the q -factorial , as
In number theory, a factorion in a given number base is a natural number that equals the sum of the factorials of its digits. [ 1 ] [ 2 ] [ 3 ] The name factorion was coined by the author Clifford A. Pickover .
Start by setting [4] = = = + Then iterate + = + + = (+) + + = (+ +) + + + Then p k converges quadratically to π; that is, each iteration approximately doubles the number of correct digits.The algorithm is not self-correcting; each iteration must be performed with the desired number of correct digits for π 's final result.
In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n.