A numerical semigroup is a subset 
of the nonnegative integers
that contains zero, is closed under addition,
and has a finite complement
in that set. Thus it is an additive monoid,
despite the customary name (Kaplan 2017). Its gaps are the nonnegative
integers outside 
, and its genus 
is their number. For example, the monoid
generated by 3 and 5 is 
and has gaps 1, 2, 4, and 7, so its genus
is 4.
The numbers 
of numerical semigroups of genus 
, 1, 2, ... are 1, 1, 2, 4,
7, 12, 23, 39, 67, 118, ... (OEIS A007323).
The Bras-Amorós conjecture concerns
the growth and monotonicity of these counts.
