[seqfan] Re: An old sequence from van der Poorten

[Max Alekseyev]

Vladimir,
I do not see equivalence here. The 3x+1 conjecture indeed implies that
A261690 is a permutation, but in the opposite direction it is not obvious
at all. Can you prove it?
Max
On Aug 28, 2015 2:50 PM, "Vladimir Shevelev" <shevelev at bgu.ac.il> wrote:

> Dear Neil,
>
>  I submitted A261690 which is an
> analog of A109732 such that the
> statement ' the sequence is a
> permutation of the positive integers
> not divisible by 3' is equivalent to
> the (3*n+1)-conjecture on numbers
> not divisible by 3.
> So I think that Van der Poorten's
> question is in the same degree unprovable
> as the (3*n+1)-conjecture.
>
>
> Best regards,
> Vladimir
>
> ________________________________________
> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Neil Sloane [
> njasloane at gmail.com]
> Sent: 27 August 2015 20:39
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] An old sequence from van der Poorten
>
> Dear Seq Fans:
>
> An old sequence suggested by a posting by Alf van der Poorten is A109732:
> a(1) = 1; for n>1, a(n) is the smallest number not already present which is
> entailed by the rules (i) k present => 2k+1 present; (ii) 3k present => k
> present.
> The open question is whether every odd number appears.
>
> It seems that numbers of the form 2^k+1 take an exceptionally long time to
> appear - see A261414, which needs more terms. In particular, when does 1025
> appear in A109732?
>
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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