"Logan's Run" by William F. Nolan on Goodreads first published in 1967

 At this link:  Logan's Run by William F. Nolan | Goodreads

"The bestselling dystopian novel that inspired the 1970s science-fiction classic starring Michael York, Jenny Agutter, and Richard Jordan.In 2116, it is against the law to live beyond the age of twenty-one years. When the crystal flower in the palm of your hand turns from red to black, you have reached your Lastday and you must report to a Sleepshop for processing. But the human will to survive is strong—stronger than any mere law.   Logan 3 is a Sandman, an enforcer who hunts down those Runners who refuse to accept Deep Sleep. The day before Logan’s palmflower shifts to black, a Runner accidentally reveals that he was racing toward a Sanctuary. With this information driving him forward, Logan 3 assumes the role of the hunted and becomes a Runner."