Looking for a formula to represent the sequence $2,4,2,8,2,4,2,16,2,4,2,8,\dots$ Is there a formula with which I can represent the sequence $2,4,2,8,2,4,2,16,2,4,2,8,\dots$?
 A: Let $P_n$ denote the number of zeros at the end of the binary representation of $n$.
Note that $P_n$ also gives the number of times that $n$ is divisible by $2$.
Your sequence can be represented as: $$a_n=2^{P_n+1}$$
A: Go to oeis.org  (Online Encyclopedia of Integer Sequences)
Put 2,4,2,8,2,4,2,16,2,4,2,8 into the box
click the "Search" button
get two different named sequences that contain this:
A209675, the Radon function at even positions
A171977, a(n) = 2^(k+1) where 2^k is the highest power of 2 dividing n
An added bonus: this will often give you additional properties, references, and remarks about the sequence
A: Hint: Consider the prime factorizations of the even numbers.
A: you can also look it up here. You just need to enter enough terms of your sequence. If you don't find it, it may mean that it is a new sequence ( or that it shares few terms with some other sequence ).
https://oeis.org/
and here it is:
https://oeis.org/search?q=2%2C4%2C2%2C8%2C2%2C4%2C2%2C16%2C2%2C4%2C2%2C8%2C...&language=english&go=Search
