In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number...

repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration...

procedures: Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to 9 or a multiple of 9. The result...

digital sum: The digit sum - add the digits of the representation of a number in a given base. For example, considering 84001 in base 10 the digit sum would...

number) in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known...

last digit. With the payload, start from the rightmost digit. Moving left, double the value of every second digit (including the rightmost digit). Sum the...

the sum of its digits is divisible by 3 (or 9). Adding the digits of a number up, and then repeating the process with the result until only one digit remains...

an even digit followed by a 1; if the last digit of a number is 2 or 8, its square ends in an even digit followed by a 4; if the last digit of a number...

last two digits. Except for cubes divisible by 5, where only 25, 75 and 00 can be the last two digits, any pair of digits with the last digit odd can occur...

visually demonstrated in the following sum, which represents T 4 + T 5 = 5 2 {\displaystyle T_{4}+T_{5}=5^{2}} as digit sums: 4 3 2 1 + 1 2 3 4 5 5 5 5 5 5 {\displaystyle...

A very simple check digit method would be to take the sum of all digits (digital sum) modulo 10. This would catch any single-digit error, as such an error...

check digit (which is the last digit of the 10-digit ISBN) must range from 0 to 10 (the symbol 'X' is used for 10), and must be such that the sum of the...

α {\displaystyle \alpha } and β {\displaystyle \beta } have the same digit sum and hence the same remainder modulo b − 1 {\displaystyle b-1} . Therefore...

A sum-product number in a given number base b {\displaystyle b} is a natural number that is equal to the product of the sum of its digits and the product...

where it is written in standard notation with k+1 digits ai as: n = ∑ i = 0 k a i b i {\displaystyle n=\sum _{i=0}^{k}a_{i}b^{i}} with, as usual, 0 ≤ ai < b...

+= weights[i] * int(digit) sum = 11 - (sum % 11) if sum == 10: sum = 0 elif sum == 11: sum = 5 return sum function getCheckDigit(num) { const weights...

sum of all n-choose binomial coefficients is equal to 2n. Consider the set of all n-digit binary integers. Its cardinality is 2n. It is also the sums...

equation, then it is not a valid UPC-A. The UPC-A check digit may be calculated as follows: Sum the digits at odd-numbered positions (first, third, fifth,.....

million digits. The Electronic Frontier Foundation also offers $150,000 and $250,000 for primes with at least 100 million digits and 1 billion digits, respectively...

case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary representation of a given number and the ℓ₁ norm of a bit...

anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. In sets...

mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence...

The last digit of a fourth power in decimal can only be 0 (in fact 0000), 1, 5 (in fact 0625), or 6. In hexadecimal the last nonzero digit of a fourth...

10th star number (whose digit sum also adds to 10 in decimal). There are exactly 100 prime numbers in base-ten whose digits are in strictly ascending...

{\displaystyle b} is a number that is the sum of its own digits each raised to the power of the number of digits. Let n {\displaystyle n} be a natural number...

n ! ⋅ t n {\displaystyle {\frac {1}{\cosh t}}={\frac {2}{e^{t}+e^{-t}}}=\sum _{n=0}^{\infty }{\frac {E_{n}}{n!}}\cdot t^{n}} , where cosh ⁡ ( t ) {\displaystyle...

use of a 0 digit in place-value notation (within other numbers) dates back as early as 700 BCE by the Babylonians, who omitted such a digit when it would...

years' digits. Since the asset has a useful life of 5 years, the years' digits are: 5, 4, 3, 2, and 1. Next, calculate the sum of the digits: 5+4+3+2+1=15...

number that cannot be written as the sum of any other natural number n {\displaystyle n} and the individual digits of n {\displaystyle n} . 20 is a self...

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...