Perfect digital invariant Sideways sum Smith number Sum-product number Bush, L. E. (1940), "An asymptotic formula for the average sum of the digits of...

In number theory, a perfect digit-to-digit invariant (PDDI; also known as a Munchausen number) is a natural number in a given number base b {\displaystyle...

number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Weisstein, Eric W. "Narcissistic Number". MathWorld. Perfect and PluPerfect...

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with...

Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Kaprekar 1955. Kaprekar 1980...

theory, a perfect digital invariant (PDI) is a number in a given number base ( b {\displaystyle b} ) that is the sum of its own digits each raised to a given...

mathematics, the Digit-reassembly numbers, or Osiris numbers, are numbers that are equal to the sum of permutations of sub-samples of their own digits (compare...

over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy numbers is not clear. Happy numbers were brought to the attention...

is a perfect sixth power (in this case 26). The last digits of each 3rd power are: It is, however, easy to show that most numbers are not perfect cubes...

integer m in a given base b that is b digits long, and each digit d at position n (the most significant digit being at position 0 and the least significant...

sum of any other natural number n {\displaystyle n} and the individual digits of n {\displaystyle n} . 20 is a self number (in base 10), because no such...

rightmost (least significant) digits follow the pattern 1–7–9–7–1 (repeating with period 5). This follows from the last digit of the triangle numbers (sequence...

A000583 in the OEIS). The last digit of a fourth power in decimal can only be 0, 1, 5, or 6. In hexadecimal the last nonzero digit of a fourth power is always...

cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the six-digit number 142857, whose first six...

In mathematics, an almost perfect number (sometimes also called slightly defective or least deficient number) is a natural number n such that the sum...

Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number "Generalized Dudeney Numbers"...

constant Kaprekar number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Richard S. Bird (1998). "Meertens...

numeral system, is the result of a non-trivial expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×...

equivalent to the handshake problem and fully connected network problems. One way of calculating the depreciation of an asset is the sum-of-years' digits method...

chosen large number being prime is inversely proportional to its number of digits, that is, to its logarithm. Several historical questions regarding prime...

itself has to be prime. He also says (wrongly) that the perfect numbers end in 6 or 8 alternately. (The first 5 perfect numbers end with digits 6, 8, 6,...

Kaprekar number Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Sloane, Neil, "A014080", On-Line...

Fibonacci-like digit) is a natural number n {\displaystyle n} in a given number base b {\displaystyle b} with k {\displaystyle k} digits such that when...

(single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum...

number Kaprekar number Digit sum Persistence of a number Perfect digital invariant Happy number Perfect digit-to-digit invariant Factorion Emirp Palindromic...

constant Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Iannucci (2000) D. R. Kaprekar...

10-choose-3 binary numbers with ten digits that include exactly three 1s). Currently, powers of two are the only known almost perfect numbers. The cardinality of...

Fibonacci numbers with d decimal digits. More generally, in the base b representation, the number of digits in Fn is asymptotic to n log b ⁡ φ = n log ⁡ φ log...

in the OEIS) For any integer n, the last decimal digit of n5 is the same as the last (decimal) digit of n, i.e. n ≡ n 5 ( mod 10 ) {\displaystyle n\equiv...

number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 (one billion...