[seqfan] Re: numbers whose cube is a palindrome

[Vladimir Shevelev]

Using table by Noe-De Geest, I noticed, that all numbers {a(n)=A002780(n);  11<=a(n)<=10^17+10^16+11}, except of 2201, allow a partition into 3 disjoint classes of terms of the following forms: 1) 10^k+1; 2) 10^(2*k)+10^k+1; 3) (10^u+1)*(10^v+1). 
The question arises, whether exists a term a(n)>10^17+10^16+11 which is in none of these classes?
If such terms do not exist, then we conclude that the sum of digits of a(n) not exceeds 4 (more exactly, it is i+1,where i  is the number of class).
This problem has not an absurd character. E.g., I have a long proof that there does not exist a(n) (other than 2201) with the sum of digits 5.
 
Regards,
Vladimir


----- Original Message -----
From: Matevž Markovič <matevz.markovic.v at gmail.com>
Date: Friday, May 20, 2011 22:53
Subject: [seqfan] Re: numbers whose cube is a palindrome
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>

> > I added a comment about Hans's search to the entry (A002760).
> > I hope I have stated the results of these searches correctly - 
> please> check! In future, it would be safer if whoever extends 
> the search
> > makes the update himself.
> >
> 
> Did you mean A002780? The idea that we update the sequence 
> ourselves is the
> right way to do it, I feel.
> 
> Anyway, now there is unneeded inf in this sequence.
> 
> <Start>
> "There are no further non-palindromic terms (other than 2201) up 
> to 10^11. -
> Matevz Markovic, Apr 04 2011. There are none up to 10^15, by 
> direct search.
> - Charles Greathouse, May 16 2011
> There are no non-palindromic terms in the range 10^15 to 10^20 
> with digits
> from the set {0,1,2}. - Hans Havermann, May 18 2011."
> <End>
> 
> I suggest that we compact them into something more readable, 
> like the latest
> search limit and who conducted it in the past, like such:
> 
> <Start>
> "There are no further non-palindromic terms up to 10^15 (Matevz 
> Markovic -
> 10^11, Charles Greathouse - 10^15, May 16 2011).
> There are no further non-palindromic terms in the range from 
> 10^15 to 10^20
> with digits from the set {0,1,2} (Hans Havermann, May 18 2011)."
> <End>
> 
> What do you think?
> 
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> 

 Shevelev Vladimir‎