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

[M. F. Hasler]

>> 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