Start with any number less than 20. If number is even, halve it and If number is odd, add one. Do they always end in 1?

Question

Start with any number less than 20. If the number is even, halve it. If the number is odd, add one. Continue using the same rules writing each number one after the other. e.g. 17, 18, 9, 10, 5, 6, 3, 4, 2, 1.

Do they always end in 1? What is the longest list of numbers?

Answer 1

yes they always end in 1
example 19
add one =20; now even half it by 2=10; now even again half it equals 5; now odd add one = 6;, half it=3; now add 1 =4; divide by 2=2,
now even divide by two equals 1