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Signed-digit representation can be used to accomplish fast addition of integers because it can eliminate chains of dependent carries. [1] In the binary numeral system, a special case signed-digit representation is the non-adjacent form, which can offer speed benefits with minimal space overhead.
While base ten is normally used for scientific notation, powers of other bases can be used too, [25] base 2 being the next most commonly used one. For example, in base-2 scientific notation, the number 1001 b in binary (=9 d) is written as 1.001 b × 2 d 11 b or 1.001 b × 10 b 11 b using binary numbers (or shorter 1.001 × 10 11 if binary ...
7 = 111 2, 13 = 111 3, 31 = 11111 2 = 111 5, 43 = 111 6, 73 = 111 8, 127 = 1111111 2, 157 = 111 12, ... (sequence A085104 in the OEIS ) While the sum of the reciprocals of the prime numbers is a divergent series, the sum of the reciprocals of the Brazilian prime numbers is a convergent series whose value, called the "Brazilian primes constant ...
The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X. For example, take the ISBN 0-201-53082-1: The sum of products is 0×10 + 2×9 + 0×8 + 1×7 + 5×6 + 3×5 + 0×4 + 8×3 + 2×2 + 1×1 = 99 ≡ 0 (mod 11). So ...
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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.
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The classes 10n+d (d = 1, 3, 7, 9) are primes ending in the decimal digit d. 2n+1: 3, 5, 7, 11, 13, ... All prime numbers from 31 to 6,469,693,189 for free download.