Q: Association A049591 and A105399

zak seidov zakseidov at yahoo.com
Thu Jan 24 08:13:50 CET 2008

```see also
A067774  Primes p such that p+2 is not a prime.
Zak

--- Tanya Khovanova <mathoflove-seqfan at yahoo.com>
wrote:

> 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
> >
>
>

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