# %C A068690: 2 is not compatible with {3,5,7}.

Mitch Harris maharri at gmail.com
Mon Dec 10 17:14:05 CET 2007

I don't know if I disagree. I read 'except' as an exclusive or, so
that the last digit would be in the complement of the property being
'excepted'. So my initial reaction was to exclude '2'. But mine may
have been an informal reading, rather than a mathematical one.

On reading the comments for this sequence and looking up precedence of
use in the OEIS, I don't think it matters one way or the other.

But now I'm curious...does (and/or should) 'except' have the meaning
of exclusive 'or' or inclusive?

Mitch

On Dec 10, 2007 10:09 AM,  <franktaw at netscape.net> wrote:
> I disagree.  The description says that all digits except the last are
> even.  It doesn't say anything about what that last digit is.  So all
> one-digit primes should be included - as they are.
>
>
> -----Original Message-----
> From: zak seidov <zakseidov at yahoo.com>
>
> %I A068690
> %S A068690
> 2,3,5,7,23,29,41,43,47,61,67,83,89,223,227,229,241,263
> %N A068690 Primes with all even digits except the
> least significant digit.
> %C A068690 2 is not compatible with {3,5,7}. Or 2 or
> {3,5,7} should be omitted.-
> Zak Seidov (zakseidov(AT)yahoo.com), Dec 10 2007.
>
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--
Mitch Harris

lq> From seqfan-owner at ext.jussieu.fr  Mon Dec 10 15:48:23 2007
lq> Date: Mon, 10 Dec 2007 06:47:04 -0800 (PST)
lq> From: Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
lq> Subject: Permutations/ Same Sequence Of Signs As Inverses
lq> To: seqfan at ext.jussieu.fr
lq> Cc: qq-quet at mindspring.com
lq> ...
lq> Consider the permutations
lq> (p(1),p(2),p(3),...p(n)) of (1,2,3,...n).
lq> We can list the (n-1) signs (+ or -) of the
lq> differences between consecutive elements of the
lq> permutations.
lq>
lq> So, for example, if we have this permutation of
lq> the first 7 positive integers: (3,2,1,7,5,6,4),
lq> the signs would be --+-+-.
lq> In other words, the kth sign is the sign of
lq> p(k+1)-p(k).
lq>
lq> So, what is the number of permutations of
lq> (1,2,3,...n) where each permutation and its
lq> inverse permutation both have the same sequence
lq> of signs?
lq>
lq> For example, for n = 6, we can have the
lq> permutation and its inverse:
lq> 4,2,6,3,5,1
lq> 6,2,4,1,5,3
lq>
lq> Both permutations have the sequence of signs:
lq> -+-+-
lq>
lq> Of course, if a permutation is its own inverse,
lq> then it has the same sequence of signs as its
lq> inverse.
lq>
lq> Could someone please calculate more terms of the
lq> sequence where the nth term equals the number of
lq> such permutations of the first n positive
lq> integers?
lq> I get the sequence beginning 1,2,4,10,... (The
lq> permutations for n = 1 through 4 or 5 that fit
lq> the conditions are all inverses of themselves.
lq> The case is different for 6, obviously, given the
lq> example above.)
lq>
lq> Is this sequence in the EIS already?
lq> ....

I get 1,2,4,10,26,80,272,1076,4848,24832,142340,902440

with a brute force C++ program which scans all permutations:

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

// return inverse permutation of s
vector<int> invsPerm( const vector<int> & s)
{
}

inline int k(const vector<int> & s)
{
}

int main(int argc, char *argv[])
{
}