I found an amazing circle while surfing on the internet.(I will call this circle a 32-AC.) It is a circle with 32 numbers with no numbers written twice. Also, the sum of any two adjacent numbers is a square number. I will just write it in a row.
$\displaystyle 1-8-28-21-4-32-17-19-30-6-3-13-12-24-25-11-5-31-18-7-29-20-16-9-27-22-14-2-23-26-10-15-1$
You can try adding any adjacent two numbers and check that the result is square number.
$9-36-49-25-36-49-36-49-36-9-16-25-36-49-36-16-36-49-25-36-49-36-25-36-49-36-16-25-49-36-25-16$
Maybe many people will know this circle, but my question is that "Is a 32-AC a smallest AC?", "Is there any n-AC such that n $\neq$ 32?", and "What is the pattern in the n-AC?".
If you have found any n-AC or have answered my question above, please answer it.
The n-AC definition were these.
(1)The n-AC should contain all the number 1~n only once.
(2)The sum of the two adjacent number should be a square number.