Permutations of 0-to-n with prime sums of adjacent terms, or Square chains with zero

[Max]

zak seidov wrote:
> Dear Seqfans,
> In A090460 and A071983,
> permutations of 1-to-n with prime sums of adjacent
> terms are considered. 

According to the definitions of those sequences, the sums should be square not prime.

> But what if also zero is included?
> 
> For n=15 we have one 0-to-15 solution (1 for 1-15),

I'm not sure what you're computing.
I've got the following:
# of permutations of {0,...,15} where sums of adjacent elements are prime = 2358024
# of permutations of {0,...,15} where sums of adjacent elements are square = 6

# of permutations of {0,...,15} starting with 0 and ending with 15 where sums of adjacent elements are prime = 125868
# of permutations of {0,...,15} starting with 0 and ending with 15 where sums of adjacent elements are square = 0

Max


> for n=16 we have two 0-to-16 solutions (1 for 1-16),
> for n=17 we have two 0-to-17 solutions (1 for 1-17),
> for n=18-22 no soln,
> for n=23 we have four 0-to-23 solutions (3 for 1-23),
> for n=24 no soln, 
> for n=25 we have 12 0-to-25 solutions (10 for 1-25),
> for n=26 we have 14 0-to-25 solutions (12 for 1-26), 
> etc.
> 
> Could someone (T.D.Noe?) please check/calculate this,
> thanks,
> Zak
> 
> 
> 
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