# [seqfan] Re: Fwd: Your A051217 Nonnegative numbers of the form 6^x-y^2.

Charles Greathouse charles.greathouse at case.edu
Thu Nov 17 08:28:50 CET 2011

```David Wilson verified the sequence through 1152 and I did similarly
through 10^11.  I can't prove that it's computable in general (thanks
for correcting my terminology here, David) but I strongly suspect it
is.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Nov 16, 2011 at 5:11 PM, Vladimir Shevelev <shevelev at bgu.ac.il> wrote:
> I agree with David: the sequence is, of course,  well-defined. But it is clear that without an upper estimate for x it cannot be computable. Since till now such an estimate is unknown, then we should use an empirical conjecture. For example, one can conjecture that, for the n-th term of the sequence, x  not exceeds n. In such case one can  write in the title "a(1)=0; for n>=2, a(n) is the least number >a(n-1) of the form 6^x-y^2 with x<=n  and a(n)=0, if such number does not exist". Then, e.g.,  23  pretending to be a(8)  is verified under condition  6^x-y^2-23=0, x=1,...,8. Now this sequence is  well-defined and well computable. In a comment one can pose a conjecture:" It is a monotone sequence containing all numbers of the form 6^x-y^2".
>
> Regards,
>
> ----- Original Message -----
> From: David Wilson <davidwwilson at comcast.net>
> Date: Tuesday, November 15, 2011 1:53
> Subject: [seqfan] Re: Fwd: Your A051217 Nonnegative numbers of the form 6^x-y^2.
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>
>> Stop using that terminology.
>>
>> The sequence is perfectly well-defined.
>> n >= 0 is in the sequence iff it is of the form 6^x - y^2.
>> Every n >= 0 is either of this form or it is not.
>>
>> The question is, is the sequence computable?
>> Specifically, is there an algorithm that determines if n is in
>> or out of
>> the sequence?
>>
>> The real question is,
>>
>> On 11/11/2011 9:57 AM, Charles Greathouse wrote:
>> > No, scratch that.  I can show that the sequence is well-defined
>> > through ten million.  No general proof yet, though.
>> >
>> > Charles Greathouse
>> > Analyst/Programmer
>> > Case Western Reserve University
>>
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