# Permutations Coprime &...

[Leroy Quet]

I have discussed a less-limiting variation of this problem before 
(sans the a(k-1)+a(k+1) coprime to a(k) condition).

For every positive integer n, what are the number of permutations,
a(1),a(2),a(3),...,a(n),
of {1,2,3,...,n}

where GCD(a(k),a(k+1)) = 1 for all k, 1<=k<=n-1;

AND where, as well,
GCD(a(k),a(k-1)+a(k+1)) = 1 for all k, 2<=k<=n-1?

I think the sequence begins:
1, 2, 2, 2,...

Thanks,
Leroy Quet