[seqfan] Re: A182514(7)?

[Charles Greathouse]

I don't think that "A182514 is a subsequence of A111870" can be justified
at present.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Fri, Apr 25, 2014 at 9:13 PM, John W. Nicholson
<reddwarf2956 at yahoo.com>wrote:

> Because A111870 also appears to be a subset of A205827, does the same
> observation hold for it? Maybe instead of A205827 the comment should have
> stated 'subset of A111870' which in turn is a subset of A205827?
>
>
> John W. Nicholson
> On Friday, April 25, 2014 11:07 AM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
> I should also mention that one of the comments appears to be wrong, or at
> >least unproven. There's no reason to suppose, a priori, that this is a
> >subsequence of A205827. Suppose p is in A182514, with the next prime q = p
> >+ g (with g "unusually large"). Then it is plausible that some nearby
> prime
> >p' followed by a prime q' = p' + g - 2 with p' not in A205827, but p'
> still
> >in A182514.
> >
> >Extreme case: suppose the 10^100-th prime is followed by a gap of 10^50
> >before the next prime, which is consistent with current knowledge (even
> >under the RH). Clearly this prime is in A182514. But if the (10^100 +
> >10)-th prime was followed by a gap of 'only' 10^49 it would still be in
> the
> >sequence, even though it wouldn't be in A205827.
> >
> >Charles Greathouse
> >Analyst/Programmer
> >Case Western Reserve University
> >
> >
> >
> >On Fri, Apr 25, 2014 at 11:42 AM, Charles Greathouse <
> >charles.greathouse at case.edu> wrote:
> >
> >> I think that it exists and is greater than 10^18.
> >>
> >> Charles Greathouse
> >> Analyst/Programmer
> >> Case Western Reserve University
> >>
> >>
> >> On Fri, Apr 25, 2014 at 8:51 AM, John W. Nicholson <
> reddwarf2956 at yahoo.com
> >> > wrote:
> >>
> >>> Has anyone got a clue as to the value of a(7) of A182514,
> >>> https://oeis.org/A182514 , or even if it exist?
> >>>
> >>>
> >>> John W. Nicholson
> >>>
> >>> _______________________________________________
> >>>
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>
> >>
> >
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