Actually the candle is red, but the video and the photo are purplish.

Arduino code:

 
#include <Adafruit_NeoPixel.h>

const int pinNumber = 6;    // Pin number of the DIN line to the neoPixels
const int pixelCount = 9;   // number of pixels
int level = 100;            // the white LED color for the whole strip

// declare the strip of pixels:
Adafruit_NeoPixel strip = Adafruit_NeoPixel(pixelCount, pinNumber, NEO_GRBW + NEO_KHZ800);

void setup() {
  strip.begin();    // initialize pixel strip
  strip.clear();    // turn all LEDs off
  strip.show();     // Initialize all pixels to 'off'
}

void loop() {
  for (int brightness = 150; brightness <= 255; brightness++) {
      strip.setBrightness(brightness);    // set the brightness
      strip.setPixelColor(0, 0,26,255);
      strip.setPixelColor(1, 255,0,0);
    strip.show();                             // refresh the strip
    delay(5);                               // wait a hundredth of a second
  }
  for (int pixel = 2; pixel < pixelCount; pixel++) {
    strip.setPixelColor(pixel, 255, 26, 0, level);// set the color for this pixel
    strip.show();    // refresh the strip

    delay(100);
    if (level < 80) 
    level = 100;
    level = level -50;
  }
 
}

Refference:

https://github.com/tigoe/NeoPixel_examples

the Adafruit_NeoPixel library

NOTE: use NEO_GRBW + NEO_KHZ800  instead of RGBW