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

[Vladimir Shevelev]

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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