[seqfan] Re: A214089

[zak seidov]

{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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