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In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
As an example, starting with the number 8991 in base 10: 9981 – 1899 = 8082 8820 – 0288 = 8532 8532 – 2358 = 6174 7641 – 1467 = 6174. 6174, known as Kaprekar's constant, is a fixed point of this algorithm. Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations. [3]
A trimorphic number or spherical number occurs when the polynomial function is () =. [1] All automorphic numbers are trimorphic. The terms circular and spherical were formerly used for the slightly different case of a number whose powers all have the same last digit as the number itself.
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 ...
The following program in Python determines whether an integer number is a Munchausen Number / Perfect Digit to Digit Invariant or not, following the convention =. num = int ( input ( "Enter number:" )) temp = num s = 0.0 while num > 0 : digit = num % 10 num //= 10 s += pow ( digit , digit ) if s == temp : print ( "Munchausen Number" ) else ...
This is a list of articles about prime numbers.A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers.
As with the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediately previous terms, thereby forming a Fibonacci integer sequence. The first two Lucas numbers are L 0 = 2 {\displaystyle L_{0}=2} and L 1 = 1 {\displaystyle L_{1}=1} , which differs from the first two Fibonacci numbers F 0 = 0 {\displaystyle F_{0}=0 ...
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