A numerical semigroup is a subset 
of the nonnegative integers that
contains zero, is closed under addition, and has a finite complement. 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.
