trigger led after led at HIGH input

Other Hardware LEDs and Multiplexing
2

a minimal version, not tried to compile with leds on pin 3,4,5 should get you started.

int ledpin[3] = { 3,4,5 };
int ledcount = 3;
int currentPin = 0;  

void setup()
{
  for (int i=0; i< ledcount; i++) pinMode(ledpin[i], OUTPUT);

  for (int i=0; i< ledcount; i++) digitalWrite(ledpin[i], LOW);
}

void loop()
{
  if (digitalRead(buttonpin) == HIGH)  // assuming buttonpress => low -> high
  {
     digitalWrite(ledpin[currentPin], LOW);
     currentPin = (currentPin + 1) % ledcount;  // wraps ledpin around
     digitalWrite(ledpin[currentPin], HIGH);
  }
  delay(1000);
}