[kditruat] Candles

On your Nth birthday, you have N candles in your cake. How many candles have you burnt over the years? The answer is the triangular numbers N(N+1)/2.

On your 14th birthday, you burn your 100th candle. On your 20th birthday, 200 candles. On your 24th birthday, you've expended exactly 300 candles. Your 500th candle is in your 32nd birthday cake. On your 36th birthday, you've expended exactly 666 candles. Your 1000th candle is at age 45, 2000th at age 63, 3000th at age 77, 4000th at age 89, and candles number 4951 through 5050 at age 100. On your 141st birthday will be your 10000th candle.

Two populations may have the same average lifespan, but different expected lifetime candle consumption due to differences in variance. The variance of the lifetime candles gets you another statistical moment.