Permuations & Inverses Have Coprime Adjacent Pairs

[Leroy Quet]

At the risk of diluting the number of responses to my questions to 
seq.fan, I post yet another question.

I just submitted:
>%S A000001 0,2,2,8,4
>%N A000001 Number of permutations of (1,2,3,...,n) where each of the (n-1) 
>adjacent pairs of elements sums to a prime.
>%e A000001 For n = 5, we have the 4 permutations and the sums of adjacent 
>elements:
>1,4,3,2,5 (1+4=5, 4+3=7, 3+2=5, 2+5=7)
>3,4,1,2,5 (3+4=7, 4+1=5, 1+2=3, 2+5=7)
>5,2,1,4,3 (5+2=7, 2+1=3, 1+4=5, 4+3=7)
>5,2,3,4,1 (5+2=7, 2+3=5, 3+4=7, 4+1=5)
>%O A000001 1
>%K A000001 ,more,nonn,


I wonder how slow/fast this sequence grows. When is the next 0? Did I 
calculate even these few terms correctly? Could someone please 
calculate/submit more terms when the sequence finally appears (after Neil 
gets back)? Could someone calculate/submit the sequence of number of such 
permutations where the first and last elements must sum to a prime too 
(and so every odd term after the first is 0)?

OK. those were questionS, with an s...
:)

thanks,
Leroy Quet