[seqfan] Re: Two neighbors sum -- and odd ranks in S
njasloane at gmail.com
Wed Oct 22 22:52:15 CEST 2014
The differences a(n)-n = A249129(n)-n now form A249161.
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.
Phone: 732 828 6098; home page: http://NeilSloane.com
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..]
> 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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