[seqfan] Re: A182514(7)?

[Charles Greathouse]

> Please explain why you said "I don't think that "A182514 is a subsequence
of A111870" can be justified at present."

My last hypothetical counterexample holds mutatis mutandis. There might be
some very large prime gap followed a short while later by a slightly
shorter gap which could still be sufficient. The sequence doesn't need
records, just big gaps (which tend to be records).

> Also, is A111870 subsequence of A205827 as to the comment "Probably
A111870 is this sequence with the exception of the term a(4) = 23." in
A205827?

Certainly we shouldn't say that it *is* a subsequence, since we don't know
that to hold. I think the present comment in that sequence is perfect.

I think it is less likely that A182514 is a subsequence of A111870. I'd
have to study it a bit more carefully but I think a counterexample is quite
possible.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Sun, Apr 27, 2014 at 4:20 PM, John W. Nicholson
<reddwarf2956 at yahoo.com>wrote:

> Charles, Please explain why you said "I don't think that "A182514 is a
> subsequence of A111870" can be justified at present."
>
> Also, is A111870 subsequence of A205827 as to the comment "Probably
> A111870 is this sequence with the exception of the term a(4) = 23." in
> A205827?
>
> Maybe change the statement to something like "Sequence is probably a
> subsequence of A111870 and A205827." for A182514? Something better?
>
>
>
> John W. Nicholson
> On Saturday, April 26, 2014 11:20 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
> 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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> >> >
> >>
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