multiplesequence

Multiplesequence is a term used in mathematics and computer science to describe a sequence in which each term is a multiple of a fixed base integer. Formally, let m be a positive integer. A multiple sequence with base m is a sequence (a_n) such that for every n, there exists an integer k_n with a_n = m * k_n. The simplest case is when k_n = n, yielding the sequence of all positive multiples of m: m, 2m, 3m, 4m, ...

More generally, the k_n can follow any integer sequence. If k_n increases by 1 for each step, the resulting a_n form an arithmetic progression with common difference m. If k_n is constrained or chosen from a subset of integers, the multiple sequence may skip values or repeat multiples, depending on the construction.

Applications and variations: In number theory, multiple sequences are used to study divisibility, modular arithmetic, and lattice models. In computer science, they arise in algorithms that generate evenly spaced samples, time slots, or resource units. A sequence of multiples of a fixed modulus is also central to problems involving least common multiples and congruences.

Examples: Multiples of 5: 5, 10, 15, 20, 25. A non-consecutive example: 5, 20, 35, 10 are all multiples of 5 but not in order.

Note: The term multiple sequence is not universally standard; it is often described in terms of base multiples or as a sequence a_n = m * b_n with a fixed m and an integer sequence b_n.