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In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations.It is also called factorial base, although factorials do not function as base, but as place value of digits.
Every sequence of digits, in any base, is the sequence of initial digits of some factorial number in that base. [ 60 ] Another result on divisibility of factorials, Wilson's theorem , states that ( n − 1 ) ! + 1 {\displaystyle (n-1)!+1} is divisible by n {\displaystyle n} if and only if n {\displaystyle n} is a prime number . [ 52 ]
Let be a natural number. For a base >, we define the sum of the factorials of the digits [5] [6] of , :, to be the following: = =!. where = ⌊ ⌋ + is the number of digits in the number in base , ! is the factorial of and
3 Factorial number system. 4 Primorial number system. 5 References. ... The base for each digit is the number of corresponding units that make up the next larger unit ...
The smallest base greater than binary such that no three-digit narcissistic number exists. 80: Octogesimal: Used as a sub-base in Supyire. 85: Ascii85 encoding. This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 ...
These symbols are collectively called factorial powers. [2] The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (), where n is a non-negative integer. It may represent either the rising or the falling
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5040 (five thousand [and] forty) is the natural number following 5039 and preceding 5041.. It is a factorial (7!), the 8th superior highly composite number, [1] the 19th highly composite number, [2] an abundant number, the 8th colossally abundant number [3] and the number of permutations of 4 items out of 10 choices (10 × 9 × 8 × 7 = 5040).