[seqfan] Re: A061712

[Vladimir Shevelev]

Thanks, Tony,
your observation is useful.

Vladimir

----- Original Message -----
From: "T. D. Noe" <noe at sspectra.com>
Date: Thursday, May 13, 2010 18:50
Subject: [seqfan] Re: A061712
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> At 1:14 PM +0000 5/13/10, Vladimir Shevelev wrote:
> >Dear seqfans,
> >
> >I used the Noe's table of A061712 in order to get the following 
> sequence:>
> >%I A177768
> >%S A177768 7,15,23,31,39,63,79,95,127,175,207,255
> >%N A177768 Points of violation of monotonicity of A061712
> >%C A177768 Questions: 1)If the sequence is infinite? 2) All 
> terms up to
> >a(12) have the form 8k-1. What is the reason of this phenomenon?
> >%Y A177768 A061712
> >%K A177768 nonn
> >%O A177768 1,1
> >%A A177768 Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 13 2010
> >
> >I think that questions in %C could be interested for you.
> 
> The sequence continues:
> 
> 7,15,23,31,39,63,79,95,127,175,207,255,511,543,607,767,1023
> 
> They are all of the form 8k-1.  Note that 2^k-1 appears for 
> all 3<=k<=10
> because primes having Hamming weight 2^k-2 (with k>2) require at 
> least 3
> zeros in their binary representation.
> 
> Tony
> 
> 
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 Shevelev Vladimir‎