  Let $\mathcal{A}'$ be the set of integers missing any three fixed digits from
their decimal expansion. We produce primes in a thin sequence by proving an
asymptotic formula for counting primes of the form $p = m^2 + \ell^2$, with
$\ell \in \mathcal{A}'$.
  The proof draws on ideas from the work of Friedlander-Iwaniec on primes of
the form $p = x^2+y^4$, as well as ideas from the work of Maynard on primes
with restricted digits.
