Given a numbering $\varphi_0, \varphi_1, \dotsc$ of the unary partial recursive functions, define a PAS as $\mathbb N$ with application $x \cdot y \simeq \varphi_x(y)$. If the numbering is admissible then this PAS is a PCA.
Is there any non-admissible numbering for which this PAS is a PCA?
Admissible numbering: https://en.wikipedia.org/wiki/Admissible_numbering
PAS = partial applicative structure, a set $X$ together with a binary partial operation $x,y \mapsto x \cdot y$ on $X$, written with left associativity.
PCA = partial combinatory algebra, a PAS such that there is $k,s$ such that (1) $k \cdot x \cdot y = x$, (2) $s \cdot x \cdot y$ is always defined and (3) $s \cdot x \cdot y \cdot z \simeq x \cdot z \cdot (y \cdot z)$.