2 3 1 2 1 3

then the two 1's enclose 1 other digit, the two 2's enclose 2 other digits, and the two 3's enclose 3 other digits.

Can you find a similar arrangement using the seven pairs 1,1,...7,7?

72462354736151

There's my solution. I found it easier to put the 14 blank spaces on a sheet of paper, and start with the 7's and work my way down. I'm sure this is not the only solution. I haven't read any comments yet. One trivial extra solution is just to turn it around. One seems plenty. :)