[seqfan] Re: A061712

[T. D. Noe]

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