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

[Reinhard Zumkeller]

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
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>