Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

Random digits are collected one at a time until a given k-digit sequence is obtained, or, more generally, until one of several k-digit sequences is obtained. In the former case, a recursive formula is ...

A multi-institutional research team found the cognitive ability to represent recursive sequences occurs in humans and non-human primates across age, education, culture and species.