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One subtracts 200 from 2500 and add 4, and get n 2 = 2304. For numbers larger than 50 (n = 50 + a), add 100×a instead of subtracting it. Squaring an integer from 26 to 74. This method requires the memorization of squares from 1 to 24. The square of n (most easily calculated when n is between 26 and 74 inclusive) is (50 − n) 2 + 100(n − 25)
Append 1 to the (right) end of the number in binary (giving 2n + 1); Add this to the original number by binary addition (giving 2n + 1 + n = 3n + 1); Remove all trailing 0 s (that is, repeatedly divide by 2 until the result is odd). Example. The starting number 7 is written in base two as 111. The resulting Collatz sequence is:
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.
Lucky number. In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the Sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the remaining set, instead of their value (or position in the initial set of natural numbers). [1]
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 ...
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system ). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor ...
604,800 = number of seconds in a week; 611,953 = the 50,000th prime number; 614,656 = 28 4; 625,992 = Riordan number; 629,933 = number of reduced trees with 28 nodes; 645,120 = double factorial of 14; 646,018 = Markov number; 649,532 = number of 26-bead necklaces (turning over is allowed) where complements are equivalent
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3] Rounding errors are due to inexactness in the representation of real numbers and the ...