Our code will use FOR loops to cycle through thecolors.
The first FOR loop will go from RED to GREEN.
The second FOR loop will go from GREEN toBLUE.
The last FOR loop will go from BLUE to RED.

// Define Pins
#define BLUE 3
#define GREEN 5
#define RED 6

void setup()
{
    pinMode(RED, OUTPUT);
    pinMode(GREEN, OUTPUT);
    pinMode(BLUE, OUTPUT);
    digitalWrite(RED, HIGH);
    digitalWrite(GREEN, LOW);
    digitalWrite(BLUE, LOW);
}

// define variables
int redValue;
int greenValue;
int blueValue;

// main loop
void loop()
{
    #define delayTime 10 // fading time between colors

redValue = 255; // choose a value between 1 and 255 to change the color.
    greenValue = 0;
    blueValue = 0;

for(int i = 0; i < 255; i += 1) // fades out red bring green full when i=255
    {
        redValue -= 1;
        greenValue += 1;
        analogWrite(RED, redValue);
        analogWrite(GREEN, greenValue);
        delay(delayTime);
    }

redValue = 0;
    greenValue = 255;
    blueValue = 0;

for(int i = 0; i < 255; i += 1) // fades out green bring blue full when i=255
    {
        greenValue -= 1;
        blueValue += 1;
        analogWrite(GREEN, greenValue);
        analogWrite(BLUE, blueValue);
        delay(delayTime);
    }

redValue = 0;
    greenValue = 0;
    blueValue = 255;

for(int i = 0; i < 255; i += 1) // fades out blue bring red full when i=255
    {
        blueValue -= 1;
        redValue += 1;
        analogWrite(BLUE, blueValue);
        analogWrite(RED, redValue);
        delay(delayTime);
    }
}