# [seqfan] Re: Two neighbors sum -- and odd ranks in S

Neil Sloane njasloane at gmail.com
Wed Oct 22 22:52:15 CEST 2014

```The differences a(n)-n = A249129(n)-n now form A249161.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Email: njasloane at gmail.com

On Wed, Oct 22, 2014 at 4:29 PM, Reinhard Zumkeller <
reinhard.zumkeller at gmail.com> wrote:

> As I forgot to stop the search, I found 1 more:
>     abs(a(127730) - 127730) = abs (127739) - 127730) = abs(-9) = 9
>
> MH>  . . .  the somewhat astonishing d(m+2n-1) = -d(m)
> I don't understand ;-)  How did you find it?
> But I got
> *A249129> zipWith (\n m -> d (m + 2*n -1)) [0..]
> [2,0,6,122,922,1994,3986,29618,59234,127730]
> [-1,-1,-2,-3,-4,-5,-6,-7,-8,-9]
>
> this looks funny, but might be not so surprising
>
>
> 2014-10-22 21:56 GMT+02:00 M. F. Hasler <oeis at hasler.fr>:
>
> > >> http://oeis.org/A249129
> >
> > RZ> Concerning Max' conjecture:
> > RZ> Smallest m such that abs(a(m)-m) = n:
> > RZ> [2,0,6,122,922,1994,3986,29618,59234,... ? ? ]
> >
> > Nice, so my previous idea of m*(n) ~ 1000*2^(n-4) (in your notations)
> > was obviously a premature (under)estimation,
> > and the bound on d(n)=a(n)-n is even smaller, confirming the
> > conjecture a(n) ~ n.
> >
> > Remarkable coincidence that the next values are again close to
> > multiples of 10^3 resp.even 10^4 : 30k, 60k....
> > (I resist against the temptation to extrapolate...)
> >
> > Can you also confirm the somewhat astonishing d(m+2n-1) = -d(m)  for
> > these record values?
> >
> > --Maximilian
> >
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> >
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> >
>
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