[seqfan] Re: A214089

[Jonathan Stauduhar]

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
>>>>
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>>>>
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>>>
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>>
>   Shevelev Vladimir‎
>
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