![]() ![]() Being well-defined does not mean that the sequence is completely known. The first condition is objective while the second is subjective a sequence of interest to me might not be to you. There are just two conditions for acceptance of a sequence: it must be well-defined (and unambiguous), and it must be interesting. Each sequence is given an identifier of the form A123456 or similar. Some sequences are of vital importance, others are more light-hearted. Many sequences are well known: the sequence of squares,, cubes, and so on. There are also many sequences important in physics, chemistry, biology, astronomy and other areas of science. Many of the sequences in OEIS come from number theory and combinatorics. ![]() OEIS is the largest collection of its kind, with more than a third of a million entries, and it continues to grow rapidly. The encyclopedia is often referred to as Sloane’s. Ownership of the database has now been transferred to the OEIS Foundation. It was established by Neil Sloane while he was a researcher at AT&T Bell Labs. It goes by the name “Online Encyclopedia of Integer Sequences”, or OEIS for short. For several decades, a collection of integer sequences has been maintained and extended. Sequences all of whose terms are integers are of particular interest in many areas of both pure and applied maths. This remarkable result was proved by Leonhard Euler. The harmonic series diverges, but the sum of reciprocals of the squares converges: The question of whether an infinite series like this has a finite sum or diverges to infinity has led to some major developments in mathematical analysis. A sequence is a list of terms, for example, the sequence of natural numbersĪnd a series is a sum, such as the harmonic series For centuries, mathematicians have delighted in the study of sequences and series, and particularly those with an infinite number of terms. ![]()
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