# [C (gcc)], 34 bytes

<!-- language-all: lang-c -->

 f(a){return!a||a%4?a%8!=7:f(a/4);}

[Try it online!][TIO-m64468wu]

[C (gcc)]: https://gcc.gnu.org/
[TIO-m64468wu]: https://tio.run/##NY7LCsIwEEX3@YpppZChPiIUFNPoj7gJSWMHNJHYumn77bFVvLtzH3DN5mZMSo5rHGLT9dFnehx1UV10cczU4TQnuwrllFbkzb23DdSvzlLYtmfGyHfw0OT5O5BFNixMkoELkZMSkuq9ELIsCRl8RY47TqiUwGec247nhYV8DYTz7G9dfb7g7w8Iyab0AQ "C (gcc) – Try It Online"

It should be ok for 0 too.