A tree sequence

[N. J. A. Sloane]

same? If there is reason: a comment in A105399 and A067774 would be useful,
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Date: Wed, 23 Jan 2008 13:53:12 -0800 (PST)
From: Tanya Khovanova <mathoflove-seqfan at yahoo.com>
Reply-To: mathoflove-seqfan at yahoo.com
Subject: Re: Q: Association A049591 and A105399
To: Richard Mathar <mathar at strw.leidenuniv.nl>, seqfan at ext.jussieu.fr
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These sequences are the same except the initial 3.

A049591  	 	 Odd primes p such that p+2 is composite.

A105399  	 	 Largest prime <= numbers of the form 6k+3 (duplicates
removed).

Proof. All primes starting from 5 are of the form 6k+1 or 6k+5.

Obviously, all primes of the form 6k+1 belong to both sequences. 

The primes of the form 6k+5 belong to the first sequence iff they are
not the smallest of the twin prime pairs. For such k, 6k+7 is
composite, and because 6k+9 is composite and of the form 6m+3, such a
prime belongs to the second sequence too. The opposite is trivial/

Tanya

--- Richard Mathar <mathar at strw.leidenuniv.nl> wrote:

> 
> Dear prime aficionados: Any ideas why A049591 and A105399 are
> essentially the
> same? If there is reason: a comment in A105399 and A067774 would be
> useful,
> perhaps also in A105792...
> Is A133387 essentially a stuttering version which resumes one of
> these
> after removal of duplicates?
> 
> Richard
> http://www.strw.leidenuniv.nl/~mathar
>