A000001 1+n^3+n^5 is prime

[Artur]

Dear Seqfans,
Yesterday I was asked "If number 1 occured in this sequence infinite times  
?"
Answer and proof was much easiest as I suppoused,
Yes indeed number 1 will be occured if and only in this sequence for  
a(Prime[n]-1) <=a(A006093)>
Recent question. In which position will be occured 2 and if number of  
places is infinite
2 occured in a(3,5,8,9,11,15,20,...)
ARTUR


Dnia 13-12-2006 o 21:36:32 Artur <grafix at csl.pl> napisał(a):

> Related sequence to Zak's
> %S A000001 1,1,2,1,2,1,10,2,2,1,2,1,48,182,2,1,60,1,10,42,2,1
> %N A000001 Smallest number n such that 1+Sum(n^(2k-1)) is prime  
> k=1,2,3,4,...
> %C A000001 If number 1 occured in this sequence infinite times ?
> %e A000001 a(7)=10 becuase n=10 is smallest prime number of the kind  
> 1+n+n^3+n^5+n^7+n^9+n^11+n^13=10101010101011
> Polynomials 1+Sum(x^(2k-1)) aren't reducible
> ARTUR
>
> Dnia 13-12-2006 o 21:06:46 Gabriel Cunningham  
> <gabriel.cunningham at gmail.com> napisał(a):
>
>> Zak,
>>
>> The question is: what led you to this sequence? Were you working on
>> something else and this sequence came up? (For instance, are all the
>> solutions of some equation primes of this form?) If so, that sort of
>> information should be submitted as a comment when you submit the  
>> sequence.
>> Otherwise, the sequence is of minimal interest - why should we care  
>> about
>> primes of this form more than primes of any other form?
>>
>> And while I agree that the OEIS is full of seemingly arbitrary  
>> sequences,
>> that's never an excuse to submit one more arbitrary one!
>>
>> Gabe
>>
>>
>> On 12/13/06, zak seidov <zakseidov at yahoo.com> wrote:
>>>
>>> Dear Neil, seqfans,
>>>
>>> I have absolutely nothing against
>>> this sequence being rejected,
>>>
>>> but OEIS is full of such and
>>> much more arbitrary ones,
>>> including those appearing
>>> while OEIS being on vacation!
>>>
>>> WADR, Zak
>>>
>>> I copy this to seqfans,
>>> It'd should be useful/interesting to others.
>>> I've been constantly crying here about OEIS standards,
>>> and think that
>>> it'd be very useful/helpful/instructive etc
>>> to have a list of rejected sequences.
>>>
>>>
>>> On 12/6/06, N. J. A. Sloane <njas at research.att.com>
>>> wrote:
>>> > %S A000001
>>> 1,2,3,5,6,9,17,20,23,27,30,39,41,47,51,57,68,72,74,78,80,96,105,111,1
>>> >
>>> 13,122,126,131,132,134,137,143,144,149,153,161,174,176,182,189
>>> > %N A000001 1+n^3+n^5 is prime.
>>> >
>>> > Zak, this seems too arbitrary
>>> >
>>> > also, did you see my note about the OEIS being on
>>> vacation?
>>> > that includes you!
>>> >
>>>
>>>
>>>
>>>
>>> ____________________________________________________________________________________
>>>
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>>> www.Answers.yahoo.com<http://www.answers.yahoo.com/>.  Try
>>> it now.
>>>
>
>
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