Consider the function defined by
T(n) = {(3n+1)/2 for n odd
{n/2 for n even
The 3n+1 conjecture is the claim that starting from any integer n>1, the sequence of iterates T(n), T(T(n)), T(T(T(n))), …, eventually reaches the integer 1 and subsequently runs through the values 1 and 2. This has been verified for all n≤10¹⁶. Confirm the conjecture in the cases n=21 and n=23.