MathDB

Shirley has a magical machine. If she inputs a positive even integer

n

, the machine will output

n/2

, but if she inputs a positive odd integer

m

, the machine will output

m+3

. The machine keeps going by automatically using its output as a new input, stopping immediately before it obtains a number already processed. Shirley wants to create the longest possible output sequence possible with initial input at most

100

. What number should she input?

Problem Statement