[seqfan] Re: A020497 name needs improvement

Charles Greathouse charles.greathouse at case.edu
Tue Jun 4 17:26:09 CEST 2013


What about "The minimal y such that there are n elements of {1, ..., y}
with fewer than p distinct elements mod p for all prime p."? That way we're
not relying on conjectures to define the sequence.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Tue, Jun 4, 2013 at 11:13 AM, T. D. Noe <noe at sspectra.com> wrote:

> 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
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
>
>
> _______________________________________________
>
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>


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