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Problems involving arithmetic progressions are of interest in number theory, [1] combinatorics, and computer science, both from theoretical and applied points of view. Largest progression-free subsets
An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
Download as PDF; Printable version; ... This is a list of notable integer sequences with links to their entries in the On-Line ... Positive integer solutions of x 2 ...
Sequences is a mathematical monograph on integer sequences. It was written by Heini Halberstam and Klaus Roth , published in 1966 by the Clarendon Press , and republished in 1983 with minor corrections by Springer-Verlag .
Sequences dn + a with odd d are often ignored because half the numbers are even and the other half is the same numbers as a sequence with 2d, if we start with n = 0. For example, 6n + 1 produces the same primes as 3n + 1, while 6n + 5 produces the same as 3n + 2 except for the only even prime 2. The following table lists several arithmetic ...
(more unsolved problems in mathematics) Erdős' conjecture on arithmetic progressions can be viewed as a stronger version of Szemerédi's theorem. Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture.
For example, the sequence,,,,, … is not an arithmetic progression, but is instead generated by starting with 17 and adding either 3 or 5, thus allowing multiple common differences to generate it. A semilinear set generalizes this idea to multiple dimensions – it is a set of vectors of integers, rather than a set of integers.
A solution to this problem is an example of a Kirkman triple system, [3] which is a Steiner triple system having a parallelism, that is, a partition of the blocks of the triple system into parallel classes which are themselves partitions of the points into disjoint blocks.
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