Indexes' Difference Divides Sum Of 2 Terms

[Leroy Quet]

Let b(1) = 1;

Let b(m) = lowest positive unpicked integers such that:

(m-k) divides evenly into (b(m) + b(k))

for EACH k, 1 <= k <= m-1.


I get (again, figured by hand, so not completely believable):

b(m) : 1, 2, 3, 8, 7, 54,...

(That last IS 54, not "5, 4".)


Is this sequence a permutation of the integers >= 1?

(I am not even sure it is infinite, without looking harder at the 
sequence's mathematics.)


thanks,
 Leroy  Quet