Connecting RC remote to Arduino
I fixed my problem by switching the pinMode like this:

void on(int btn) {
    pinMode(btn, OUTPUT);
    digitalWrite(btn, LOW);
}

void off(int btn) {
    pinMode(btn, INPUT);
}

void setup() {
    off(13);
}

void loop() {
    on(13);
    delay(1000);
    off(13);
    delay(1000);
}