Permutations: Adjacent Elements Sum to Primes

[James Buddenhagen]

----- Original Message ----- 
From: "Leroy Quet" <qq-quet at mindspring.com>
To: <seqfan at ext.jussieu.fr>
Sent: Saturday, March 26, 2005 1:11 PM
Subject: Permutations: Adjacent Elements Sum to Primes


> I wonder if this sequence is already in the database, perhaps with a 
> different definition.
> 
> a(n) = number of permutations,[p(1),p(2),...,p(n)],
> of [1,2,3,..,n] where p(1)+p(2), p(2)+p(3), p(3)+p(4),...,p(n-1)+p(n)
> are each equal to primes.
> 
> I get, by hand, the sequence beginning
> 0, 2, 2, 8, 4,...
> 
> (offset = 1)
> 
> For example,
> 5, 2, 1, 4, 3
> is a permutation included in the count for n=5.
> 
> thanks,
> Leroy Quet

Yes. A051239 is your sequence, each term divided by 2, and starting at 1.

Jim Buddenhagen