[seqfan] Re: A214089

[Robert G. Wilson v]

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
>>  >>
>>  >> ______________________________**_________________
>>  >>
>>  >> Seqfan Mailing list - http://list.seqfan.eu/  >>  >  >
>> 
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>> 
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> 
> Shevelev Vladimir‎
> 
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