divideshigh

Divideshigh is a term used in recreational mathematics to describe a pattern in integer sequences in which successive terms exhibit strong divisibility relationships. In its informal usage, a sequence a1, a2, a3, ... is described as divideshigh if each term beyond the first is divisible by its predecessor and the quotient a_{n+1} / a_n exceeds a specified threshold. The concept is typically employed to explore growth behavior driven by divisibility rather than simple arithmetic progression, and it often features in puzzle design and classroom activities that emphasize prime factorization and divisibility chains.

In practice, divideshigh serves as a heuristic for identifying sequences with rapid divisibility growth. It is not a formal axiom in standard number theory, but rather an exploratory idea used to categorize sequences and to motivate problems about factors, multiples, and the distribution of prime powers. The term is also used in online educational communities and puzzle forums as a label for challenges and explanations that center on divisibility patterns; in some contexts it has appeared as the name of collaborative projects or article series that collect such problems.

See also: divisibility, multiples, number theory, integer sequences.