[seqfan] Re: Natural angry numbers

[franktaw at netscape.net]

If the requirement is that the neighbor must be at least n away, 
instead of more than n away, the first packing method gives A072009.  
The corresponding sequence for the second approach is not in the 
database.

A065186 and A065187 are also kind of similar.

One can also look for the lexically first such sequence that is also a 
self-inverse permutation.  If I haven't made any mistakes, for Eric's 
definition this starts:

1,4,8,2,10,17,25,3,19,5,21,34,13,28

while my variant starts:

1,4,7,2,9,15,3,17,5,19,30,12,25,39,6

For the rule in A065186 (consecutive integers may not be adjacent), 
this starts:

1,4,6,2,5,3

and then this pattern repeats with each block 6 larger: a(n+6)=a(n)+6.

None of these is in the database.

Franklin T. Adams-Watters

-----Original Message-----
From: Eric Angelini <Eric.Angelini at kntv.be>

Hello SeqFans,

another reordering of the Naturals (as I got no msg at all
for my former post -- sigh!);

Imagine that an angry natural number could not stand the
presence of his immediate neighbours -- thus asking them to
get away;

The acceptable "get away" distance would be given by the
said angry Natural himself;

This means that "5", for instance, would not accept to see
"4" and "6" at a shorter distance than 5 integers from him;

Sequence S(1) is one packing of such Natural angry numbers:

S(1) = 
1,4,7,2,10,13,16,3,5,.,.,8,.,.,.,6,11,.,.,.14,9,.,.,.,.,.,.,.,12,.,.,.,.,
=0
A.,.,15

S(1) is build according to the "place the Naturals first" method
-- see former msg, here:
http://www.cetteadressecomportecinquantesignes.com/UniqueSum.htm

But we could also use the other building method -- "fill the
'holes' first":

S(2) = 1,3,5,7,9,2,11,13,4,15,17,6,19,21,8,23,25,27,10,29,31,12,...

S(2) comes lexicographically first,
Best,
É.