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This is the coarsest topology that includes as open subsets the family of all arithmetic progressions: that is, arithmetic progressions are a subbase for the topology.
en.wikipedia.org His early research was in number theory, investigating such topics as primes in arithmetic progression and polynomials with many initial composite values.
en.wikipedia.org Sometimes (not in this article) the phrase may also be used about primes which belong to an arithmetic progression which also contains composite numbers.
en.wikipedia.org For instance, the sequence 5, 7, 9, 11, 13, 15 is an arithmetic progression with common difference of 2.
en.wikipedia.org In particular, the seven elements (in) before a noble gas (group 18, in) higher than helium have the number of electrons in the valence shell in arithmetic progression.
en.wikipedia.org