[seqfan] Re: A182514(7)?

John W. Nicholson reddwarf2956 at yahoo.com
Sun Apr 27 22:20:11 CEST 2014


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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