[seqfan] Re: A020497 name needs improvement

T. D. Noe noe at sspectra.com
Tue Jun 4 17:13:47 CEST 2013


Let's precede the current name with "Conjecturally, " -- a word that we see
a lot in OEIS.

Best regards,

Tony


At 11:15 AM +0000 6/4/13, Vladimir Shevelev wrote:
>I quite agree with David. For example,  if y=a(2)=3, then, for integer x,
>the set {x+1, x+2, x+3} should contain twin primes {x+1, x+3} for
>infinitely many x which is a best known unsolved problem. The name
>suggested by David seems to be suitable.
>On the other hand, even for the existing name, a(n) exists. For example,
>a(n)<=R(n)/2, where R(n) is the n-th Ramanujan primes (A104272). So,
>another suitable  name is "Hypothetically minimal values of y such that n
>primes occur infinitely often among (x+1, ..., x+y), i.e. pi(x+y)-pi(x) >=
>n for infinitely many x."
>
>Regards,
>Vladimir
>
>
>----- Original Message -----
>From: David Wilson <davidwwilson at comcast.net>
>Date: Monday, June 3, 2013 17:41
>Subject: [seqfan] A020497 name needs improvement
>To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>
>> I think the description of A020497 is incorrect as it is conjectural.
>>
>>
>>
>> I believe that A020497(n) gives smallest k such that k
>> consecutive integers
>> admits a permissible prime pattern of size n.
>>
>>
>>
>> The first Hardly-Littlewood conjecture (the k-tuples conjecture)
>> impliesthat an admissible prime pattern is satisfied by an
>> infinite number of prime
>> constellations (which implies there are an infinite number of
>> values x with
>> pi(x+a(n)) - p(x) = n). However, this is still conjectural, and
>> has not been
>> proved even for the admissible pattern (0,2), which is to say,
>> we have not
>> yet proved the twin prime conjecture. For sufficiently large k (where
>> sufficiently large is not very large), we can neither
>> demonstrate nor prove
>> that a single prime constellation satisfies a maximal admissible prime
>> pattern of size n.
>>
>>
>>
>>
>>
>>
>> _______________________________________________
>>
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
> Shevelev Vladimir
>
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>
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