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The original triple comprises the constant term in each of the respective quadratic equations. Below is a sample output from these equations. The effect of these equations is to cause the m-value in the Euclid equations to increment in steps of 4, while the n-value increments by 1.
In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. Formulas for calculating primes do exist; however, they are computationally very slow. A number of constraints are known, showing what such a "formula" can and cannot be.
A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes (250s BCE), the sieve of Sundaram (1934), the still faster but more complicated sieve of Atkin [1] (2003), sieve of Pritchard (1979), and various wheel sieves [2] are most common.
A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3.
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.
On a single-step or immediate-execution calculator, the user presses a key for each operation, calculating all the intermediate results, before the final value is shown. [1] [2] [3] On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression.
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The earliest known example of a de Bruijn sequence comes from Sanskrit prosody where, since the work of Pingala, each possible three-syllable pattern of long and short syllables is given a name, such as 'y' for short–long–long and 'm' for long–long–long.