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In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code, or BRGC. Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943.
Kaprekar's routine. In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with a number, sorts the digits into descending and ascending order, and calculates the difference between the two new numbers. As an example, starting with the number 8991 in ...
The first theorem is shown similarly; one can divide the random string into nonoverlapping blocks matching the size of the desired text and make E k the event where the kth block equals the desired string. Probabilities. However, for physically meaningful numbers of monkeys typing for physically meaningful lengths of time the results are reversed.
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most single-digit ...
For example, squaring the number "1111" yields "1234321", which can be written as "01234321", an 8-digit number being the square of a 4-digit number. This gives "2343" as the "random" number. Repeating this procedure gives "4896" as the next result, and so on. Von Neumann used 10 digit numbers, but the process was the same.
For example, the number of random version-4 UUIDs which need to be generated in order to have a 50% probability of at least one collision is 2.71 quintillion, computed as follows: n ≈ 1 2 + 1 4 + 2 × ln ( 2 ) × 2 122 ≈ 2.71 × 10 18 . {\displaystyle n\approx {\frac {1}{2}}+{\sqrt {{\frac {1}{4}}+2\times \ln(2)\times 2^{122}}}\approx 2 ...
The word is related to the famous sequence of the same name (the Fibonacci sequence) in the sense that addition of integers in the inductive definition is replaced with string concatenation. This causes the length of S n to be F n +2, the (n +2)nd Fibonacci number. Also the number of 1s in S n is F n and the number of 0s in S n is F n +1.
The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4.