PROB13.mkd

points: 15 level: Medium title: Problem 11 author: Abhay Rana nemo@sdslabs.co.in answer: 6046e73cf774dda7b4317dc37ed6e6645ebdb939

Consider a series $S(n) = $

• $S(n+1) = S(n)/2 $ if S(n) is divisible by 4
• $S(n+1) = 3 \cdot S(n)$ if S(n)%4 = 1$
• $S(n+1) = S(n)-25$ if S(n)%4=2$
• $S(n+1) = S(n)+4$ otherwise$

The series is considered to terminate when $S(n)\in {0,1}$

E.g. consider that we initialize $S(0) = 40$ This relation will generate $40, 20, 10, -15, -11, -7, -3, 1$ Here number of steps = 7 Let the number below 100,000 which produces maximum terms of the terminating series be $N$ and the number of steps = $T$

Find $N \cdot T$