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I want to solve this equation but nor NSolve nor Solve are able to do this.

Gamma[1 + 8 (-1 + r) r]/(Gamma[1 + r] Gamma[1 - 9 r + 8 r^2]) - (
 Gamma[1 + 14 r] Gamma[
   1 + 8 (-2 + r) r] HypergeometricPFQRegularized[{1, -((15 r)/2), -(
     r/2)}, {1 + (13 r)/2, 1 - (33 r)/2 + 8 r^2}, 1])/(
 Gamma[1 + r/2] Gamma[1 + (15 r)/2])==0

I want to find a solution for $r \in \mathbb{N}$, $r>2$.

NSolve[Gamma[1 + 8 (-1 + r) r]/(
  Gamma[1 + r] Gamma[1 - 9 r + 8 r^2]) - (
  Gamma[1 + 14 r] Gamma[
    1 + 8 (-2 + r) r] HypergeometricPFQRegularized[{1, -((15 r)/2), -(
      r/2)}, {1 + (13 r)/2, 1 - (33 r)/2 + 8 r^2}, 1])/(
  Gamma[1 + r/2] Gamma[1 + (15 r)/2]), r, Integers]

Any suggestion? I get the following error message:

NSolve::nsmet: This system cannot be solved with the methods available to NSolve.
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