Quadratic residue number sequences generate periodic well-depth patterns for acoustic diffusers.

Evidence

Quadratic residue sequences well depth = n2 mod p where p is a prime number. If p = 5, this gives a set of well depths of 0, 1, 4, 4, 1, 0, 1, … etc. so the sequence repeats with a period of 5. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2091

Categorization

• XREF: Connects to number theory (modular arithmetic over primes); the same sequences appear in cryptography and coding theory.