Do these sequences exist in the OEIS?
Andrew Plewe
aplewe at sbcglobal.net
Wed May 23 19:17:37 CEST 2007
In general, it is easy to see that x^2 = y^2 + m has no integer
solutions with respect to x,y if and only if m = 2 modulo 4.
Therefore, the first one of your sequences is simply A016825:
%C A016825 No solutions to a(n)=b^2-c^2 - Henry Bottomley
(se16(AT)btinternet.com), Jan 13 2001
The second sequence is A042965 or A024352, whichever you like.
Max
On 5/23/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> Good point,
>
> 3 = 1(1+2)
> 5 = 1(1+4)
> 7 = 1(1+6)
> etc.
>
> So all odd numbers should, trivially, be in the sequence. Thanks!
>
> -Andrew Plewe-
>
> -----Original Message-----
> From: Max Alekseyev [mailto:maxale at gmail.com]
> Sent: Wednesday, May 23, 2007 3:07 AM
> To: Andrew Plewe
> Cc: seqfan at ext.jussieu.fr
> Subject: Re: Do these sequences exist in the OEIS?
>
> On 5/23/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> > sequence one: integers which do not satisfy x^2 = y^2 + A(n):
> >
> > 1,2,3,4,5,6,7,9,10,13,14,17,18,19,22,23,25,26,29,30,31,34,38,etc...
> > (i.e., integers which cannot be expressed as n(n+E), where E is an even
> > integer greater than zero)
>
> Why 3 belong to this sequence?
>
> 2^2 = 1^2 + 3
> 3 = n*(n+E) for n=1, E=2.
>
> Max
>
>
>
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