Question

find the general rule to find the nth term of the series​

Answer 1

You can get an by writing n in binary and interpreting it as a base 3 number. For example, to get a21 we note that 21=101012 so a21=34+32+30=9110 One way to express this is

an=∑i=0∞3inmod2i+12i

where we are using integer division. The fraction picks out whether the ith bit in the binary representation of n is a 1.