# [seqfan] Re: Natural angry numbers

franktaw at netscape.net franktaw at netscape.net
Fri Oct 9 22:35:28 CEST 2009

```This breaks for 26, which is the first number that does not occur in
A057167; because A005132(26) = A005132(18) = 43 is the first
duplication in Recaman's sequence.

-----Original Message-----
From: John W. Layman <layman at math.vt.edu>

If the requirement is that n must be exactly n terms away from n-1,
at least n away or more than n away, I found:

1,4,2,131,129,3,5,16,14,12,10,8,6,31,29,27,25,23,...

and the next term a(19) seemed to be difficult.

Surprisingly, the sequence seems to be

A057167 <http://www.research.att.com/%7Enjas/sequences/A057167> Term in
Recaman's sequence A005132
<http://www.research.att.com/%7Enjas/sequences/A005132>
where n appears for first time, or 0 if n never appears.
1, 4, 2, 131, 129, 3, 5, 16, 14, 12, 10, 8, 6, 31, 29, 27, 25, 23,
99734, 7, 9,
11, 13, 15, 17, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42, 40, 38,
111, 22,
20, 18, 28, 30, 32, 222, 220, 218, 216, 214, 212, 210, 208, 206, 204,
202, 200,
198, 196

So it's easy to see why a(19)=99734 was difficult.

The "angry" property is not mentioned in A057167
<http://www.research.att.com/%7Enjas/sequences/A057167>.

John

Eric Angelini wrote:

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,.,.,.,.,
.,.,15

... (continued)

and

franktaw at netscape.net replied:
> 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.
>
>
>

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