[seqfan] Re: A214089

[Vladimir Shevelev]

Hi Jonathan,

Please, see A215174. You are, please, welcome to add new terms or additional comments.

Best regards,
Vladimir

----- Original Message -----
From: Jonathan Stauduhar <jstdhr at gmail.com>
Date: Sunday, August 5, 2012 0:52
Subject: [seqfan] Re: A214089
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> Hi Vladimir,
> 
> Do you plan to create an entry for this sequence of records?
> 
> Jonathan
> 
> On 8/3/2012 3:04 PM, Vladimir Shevelev wrote:
> > Consider sequence A215113 in which a(n) is the number of 
> different prime divisors of A214723(n). The records of A215113 
> begin a(1)=1, a(3)=2, a(12)=3, a(132)=4. It is interesting to 
> continue the sequence of places of records 1,3,12,132,...(and 
> the corresponding values of A214723: 8, 18, 130, 6830,...). 
> Since, as is well known, the set of the sums of two 
> squares  is closed under multiplication, then it is natural 
> to think that the sequence of records is infinite (or, the same, 
> A215113 is unbounded).
> >
> > Regards,
> > Vladimir
> >
> > ----- Original Message -----
> > From: Jonathan Stauduhar<jstdhr at gmail.com>
> > Date: Thursday, August 2, 2012 21:45
> > Subject: [seqfan] Re: A214089
> > To: Sequence Fanatics Discussion list<seqfan at list.seqfan.eu>
> >
> >> I have submitted my sequence - thank you.
> >>
> >> If you have the time, would you mind taking a look at A214723
> >> <https://oeis.org/A214723>.  I am dissatisfied with the
> >> current
> >> description (I think the language is unclear), but I am
> >> unwilling to
> >> "haggle" further.
> >>
> >> Thanks much,
> >>
> >> Jonathan
> >>
> >> On 8/2/2012 10:14 AM, Neil Sloane wrote:
> >>> The sequence derived from A118478 now has an entry of its 
> own -
> >> it is
> >>> A215021. It is certainly different from your sequence, which 
> should>>> probably also have its own entry - I suggest you 
> submit it!
> >>> Neil
> >>>
> >>> On Tue, Jul 31, 2012 at 2:03 PM, Jonathan
> >> Stauduhar<jstdhr at gmail.com>wrote:>
> >>>> Howdy,
> >>>>
> >>>> I observed that for the first 14 terms in A214089<
> >>>> https://oeis.org/A214089>   , the following holds:
> >>>>
> >>>>     p^2 - 1 / n# = 4x.
> >>>>
> >>>> In other words, p^2 - 1 / n# is congruent to 0 MOD 4.
> >>>>
> >>>> Subsequent to this observation , two new terms were added and
> >> the above
> >>>> holds true for those as well.
> >>>>
> >>>> Solving for x gives the sequence {1, 1, 1, 1, 19, 17, 1,
> >> 2567, 3350,
> >>>> 128928, 3706896, 1290179, 100170428, 39080794, 61998759572,
> >> 7833495265}.>>
> >>>> Can someone far more familiar with prime numbers explain why
> >> this may or
> >>>> may not be true for all a(n)?  I would like to add a
> >> comment to the
> >>>> sequence noting this observation, but I am unsure whether it
> >> is in fact
> >>>> true for all a(n).
> >>>>
> >>>>    I don't know if this is relevant, but I 
> found a
> >> comment, by Robert G.
> >>>> Wilson, in A118478<https://oeis.org/A118478>   which
> >> defines another
> >>>> sequence whose first seven terms are {1, 1, 1, 1, 19, 17, 1}
> >> and also has
> >>>> 39080794 as its 14th term.
> >>>>
> >>>> -Jonathan
> >>>>
> >>>> ______________________________**_________________
> >>>>
> >>>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>>
> >>>
> >> _______________________________________________
> >>
> >> Seqfan Mailing list - http://list.seqfan.eu/
> >>
> >   Shevelev Vladimir‎
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> 
> _______________________________________________
> 
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> 

 Shevelev Vladimir‎