  Given two closed oriented manifolds $M,N$ of the same dimension, we denote
the set of degrees of maps from $M$ to $N$ by $D(M,N)$. The set $D(M,N)$ always
contains zero. We show the following (non-)realisability results:
  (i) There exists an infinite subset $A$ of $\mathbb Z$ containing $0$ which
cannot be realised as $D(M,N)$, for any closed oriented $n$-manifolds $M,N$.
  (ii) Every finite arithmetic progression of integers containing $0$ can be
realised as $D(M,N)$, for some closed oriented $3$-manifolds $M,N$.
  (iii) Together with $0$, every finite geometric progression of positive
integers starting from $1$ can be realised as $D(M,N)$, for some closed
oriented manifolds $M,N$.
