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...
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Digital root (redirect from Repeated digital sum)
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...
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Casting out nines (section Digit sums)
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...
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Harshad number (section Sums of harshad numbers)
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...
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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...
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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...
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Triangular number (redirect from Sum of integers)
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...
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digit, starting from the last digit. If doubling a digit results in a value > 9, subtract 9 from it (or sum its digits). Sum all the resulting digits...
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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...
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Universal Product Code (section Number system digit)
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,.....
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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...
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number in a given number base b {\displaystyle b} that is equal to the sum of its digits each raised to the power of itself. An example in base 10 is 3435...
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ISBN (redirect from 9-digit SBN)
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...
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Depreciation (redirect from Sum-of-years' digits depreciation)
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...
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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...
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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...
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the number by the sum or product of its digits until one reaches a single digit. Because the numbers are broken down into their digits, the additive or...
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natural number with an even number of digits, that can be factored into two natural numbers each with half as many digits as the original number, where the...
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Power of two (section Last digits)
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...
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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...
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α {\displaystyle \alpha } and β {\displaystyle \beta } have the same digit sum and hence the same remainder modulo b − 1 {\displaystyle b-1} . Therefore...
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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...
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number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself...
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S10 (UPU standard) (section Check-digit calculation)
+= 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...
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{\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...
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an odd prime, count all digits greater than (p + 1) / 2; also count digits equal to (p + 1) / 2 unless final; and count digits equal to (p − 1) / 2 if...
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Parity (mathematics) (redirect from Even digit)
odd if its last digit is 1; and it is even if its last digit is 0. In an odd base, the number is even according to the sum of its digits—it is even if and...
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Hamming weight (redirect from Binary sideways sum)
case, a given set of bits, this is the number of bits set to 1, or the digit sum of the binary representation of a given number and the ℓ₁ norm of a bit...
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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...
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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...
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