We arbitrarily select a number as the first number.

Let's arbitrarily select the number 7 as the first number.

We add 3 to the 1st number 7 and get 10.
We subtract 4 from 10 and get 6.
So the 2nd number is 6.
So far we have the first 2 terms of the sequence 7,6

We add 3 to the 2nd number 6 and get 9.
We subtract 4 from 9 and get 5.
So the 3rd number is 5.
So far we have the first 3 terms of the sequence 7,6,5

We add 3 to the 3rd number 5 and get 8.
We subtract 4 from 8 and get 4.
So the 4th number is 4.
So far we have the first 4 terms of the sequence 7,6,5,4

We add 3 to the 4th number 4 and get 7.
We subtract 4 from 7 and get 3.
So the 5th number is 3.
So far we have the first 5 terms of the sequence 7,6,6,4,3

So now we see that the next term is always 1 less than the preceding
term.  Why is that?

It's because adding 3 then subtracting 4 is the same as
subtracting 1.

So other sequences that subtract 1 each time are

6,5,4,3,2,1,0,...
10,9,8,7,6,5,...
3,2,1,0,-1,-2,...
-8,-9,-10,-11,-12,-13,...
0,-1,-2,-3,-4,-5,-6,...

Edwin