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The Lucas–Lehmer test works as follows. Let M p = 2 p − 1 be the Mersenne number to test with p an odd prime. The primality of p can be efficiently checked with a simple algorithm like trial division since p is exponentially smaller than M p. Define a sequence {} for all i ≥ 0 by
An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy. It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms).
Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...
The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. It relies on bounding sums of terms in the series. This convergence criterion is named after Augustin-Louis Cauchy who published it in his textbook Cours d'Analyse 1821.
While most of the tests deal with the convergence of infinite series, they can also be used to show the convergence or divergence of infinite products. This can be achieved using following theorem: Let {} = be a sequence of positive numbers.
Convergence proof techniques are canonical patterns of mathematical proofs that sequences or functions converge to a finite limit when the argument tends to infinity.. There are many types of sequences and modes of convergence, and different proof techniques may be more appropriate than others for proving each type of convergence of each type of sequence.
Digit-span tasks can be given forwards or backwards, meaning that once the sequence is presented, the participant is asked to either recall the sequence in normal or reverse order. [8] Digit-span tasks are the most commonly used test for memory span, partially because performance on a digit-span task cannot be affected by factors such as ...
The poker test, tested for certain sequences of five numbers at a time (AAAAA, AAAAB, AAABB, etc.) based on hands in the game poker. The gap test , looked at the distances between zeroes (00 would be a distance of 0, 030 would be a distance of 1, 02250 would be a distance of 3, etc.).