More info on Conjuncture of Terros (Terras) In answering a coding problem called "Conjuncture of Terros", there was scant information on the series.
What is the origin of this series? and what might applications may use it?
See original problem
Terros number sequence
t(0) = n  
t(1) = n  
if t(n-1) is even  
  t(n) = t(n-1)/2  
else  
  t(n) = (3*t(n-1) + 1)/2

Web search of "Terros" only led to some ADHD related sites.
[Edit]
@Palec provides a corrected spelling for Riho Terras 
 A: Riho Terras (not Terros!) was American mathematician (born 1939 in Tartu, Estonia,  died 2005 in San Diego, CA, USA). Author of Terras Theorem, which is an important partial result in solving Collatz Problem, known also as 3n + 1 conjecture.
The conjecture is that given a positive integer $a_0$, iterating
$$
a_n = \begin{cases}
  \frac{1}{2} a_{n-1} & \text{for } a_{n-1} \text{ even,} \\
  3 a_{n-1} + 1 & \text{for } a_{n-1} \text{ odd}
\end{cases}
$$
always reaches 1.
Terras Theorem uses a slight modification $t_n$ of the original Collatz sequence $a_n$. It says that for almost all $t_0$ holds that $\exists n \in \mathbb{N}: t_n < t_0$ for $t_n$ defined as
$$
t_n = \begin{cases}
  \frac{1}{2} t_{n-1} & \text{for } t_{n-1} \text{ even,} \\
  \frac{1}{2} (3 t_{n-1} + 1) & \text{for } t_{n-1} \text{ odd.}
\end{cases}
$$
They are equivalent from the convergence point of view because $t_n$ is subsequence of $a_n$ obtained by deletion of values immediately following an odd value. These deleted values are always even, because the preceding value is odd and
$$
\forall k \in \mathbb{N}: 3(2k + 1) + 1 \equiv 0 \pmod{2}.
$$
When this is so much on-topic, I cannot help:

A: I would recommend searching for the Collatz Conjecture (also called 3n+1 problem). It's a more common name. A little explanation though:
You start with natural number $n$. If it's even, you go to $\frac{n}{2}$. If it is odd, you go to $3n+1$, which then will be even of course. Then repeat this process again and again. The Terros sequence is pretty much a modified Collatz sequence, just that you skip the even number $3n+1$ and directy go to $\frac{3n+1}{2}$. The interesting aspect is to find out where this sequence goes in the end. The conjecture states that for any starting point you end up in the circle $1\rightarrow4\rightarrow2\rightarrow1$. However this is not yet proven.
PS: For Terros the circle would of course be $1\rightarrow2\rightarrow1$.
