[seqfan] Re: Can a sequence that is not a linear recurrence with constant coefficients be such mod every prime p (possibly with different coefficients)?

[Georgi Guninski]

On Fri, Feb 04, 2011 at 02:31:35PM +0200, Georgi Guninski wrote:
> On Thu, Feb 03, 2011 at 04:56:35PM +0100, allouche at math.jussieu.fr wrote:
> > 
> > 
> > Am I mistaken if I give n! as an example?
> > jp
> > 
> > 
> 
> thank you. your example recurrence seems of unbounded order mod p.
> 
> is it possible the order of the recurrence mod p to be bounded?
>

appears such bounded order recurrence is impossible:
http://mathoverflow.net/questions/54315/can-an-integer-or-rational-sequence-satisfy-some-bounded-order-recurrence-mod

(this agrees with my search in a subset of OEIS, assuming my search was
sane).