We have 5 different values of n to produce 15 terms of a sequence based on n and F for each value of n. So that's 5 series we have to produce.
F(n)=n/2 for n even, F(n)=(3(n)+1)/2 for n odd.
F(6)=3; F(3)=5; F(5)=8; F(8)=4; ...
The method is to apply F to each term to find the next.
Each series degenerates with the recurring pattern 1,2 (oscillating series).
The series is:
n=6: 6, 3, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1
n=10: 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2
n=15: 15, 23, 35, 53, 80, 40, 20, 10, 5, 8, 4, 2, 1, 2, 1
n=32: 32, 16, 8, 4, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2
n=17: 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, 2