[seqfan] Re: A214089

[Vladimir Shevelev]

Thank you, Zak and Bob,

Now we  can submit together two interesting sequences with the known 7 terms!

Best regards,
Vladimir

----- Original Message -----
From: "Robert G. Wilson v" <rgwv at rgwv.com>
Date: Saturday, August 4, 2012 23:06
Subject: [seqfan] Re: A214089
To: 'Sequence Fanatics Discussion list' <seqfan at list.seqfan.eu>

> Et al,
> 
> I can extend this .
> Using the Mmca coding of:
> nn = 10^10; pp = PrimePi[Sqrt[nn]]; ps = Prime[Range[pp]]; t = 
> Sort at Flatten[Table[ps[[i]]^2 + ps[[j]]^2, {i, pp}, {j, i, pp}]]; 
> t = Select[t, # <= nn &]; t = Transpose[Select[Tally[t], 
> #[[2]] == 1 &]][[1]];
> len = Length at t; k = 1; mx = 0; While[k < 1+len, po = 
> PrimeNu[t[[k]]]; 
>  If[po > mx, mx = po; Print[{po, k, t[[k]]}]]; k++]
> 
> {1,1,8}, {2,3,18}, {3,12,130}, {4,132,6890}, {5,2074,254930}, 
> {6,18625,3352570}, {7,2138668,683351890}.
>  And no others < 24,866450.
> 
> Respectfully submitted,
> Bob.
> 
> -----Original Message-----
> From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of 
> zak seidov
> Sent: Saturday, August 04, 2012 8:38 AM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: A214089
> 
> {record n in A215113, position of record k, A214723(k)} {1,1,8} 
> {2,3,18,} {3,12,130} {4,132,6890} {5,2074,254930} 
> {6,18625,3352570} And up to A215113 (1013356), there is no new record.
> 
> 
> ----- Original Message -----
> > From: Vladimir Shevelev <shevelev at bgu.ac.il>
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Cc: 
> > Sent: Saturday, August 4, 2012 1:04 AM
> > Subject: [seqfan] Re: A214089
> > 
> > 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
> >>  >>
> >>  >> ______________________________**_________________
> >>  >>
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> >>  >  >
> >> 
> >>  _______________________________________________
> >> 
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> >> 
> > 
> > Shevelev Vladimir‎
> > 
> > _______________________________________________
> > 
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> > 
> 
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 Shevelev Vladimir‎