Sequence

If we take the numbers from 1 to 15 (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) and rearrange them in such an order that any two consecutive numbers in the sequence add up to a perfect square, we get,

8     1     15     10     6     3     13     12      4      5     11     14      2      7      9
    9    16    25     16     9     16     25     16     9     16     25     16     9     16

I ask the readers the following:

Can you take the numbers from 1 to 25 to produce such an arrangement?

How about the numbers from 1 to 100?