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An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence. The xorwow generator is the default generator in the CURAND library of the nVidia CUDA application programming interface for graphics processing units.
Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance.
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), [1] is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers.
The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.
An integer for which the average of its positive divisors is also an integer. A003601: Colossally abundant numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... A number n is colossally abundant if there is an ε > 0 such that for all k > 1,
A linear congruential generator with base b = 2 32 is implemented as + = (+) , where c is a constant. If a ≡ 1 (mod 4) and c is odd, the resulting base-2 32 congruential sequence will have period 2 32.
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.