clearvars,clc

palTrip=double.empty(0);

palOdo=double.empty(0);

for i=0:99

  s=sprintf('%03d',10*i+floor(i/10));

  palTrip(i+1)=str2double(s);

end

trip=zeros(1,1000);

trip(palTrip+1)=1;

trip=repmat(trip,1,200);

for i=0:999

  s=sprintf('%03d',i);

  s=[s s(2) s(1)];

  palOdo(i+1)=str2double(s);

end

palOdo=[palOdo palOdo+100000];

odo=zeros(1,200000);

odo(palOdo+1)=1;

for offset=0:999

   hits=trip & odo;

   hits=find(hits);

   if length(hits)==0

     break

   end

   spans=hits(2:end)-hits(1:end-1);

   fmax=find(spans==max(spans));

   disp([offset max(spans) ])

   trip=[trip(2:end) trip(1)];

end

finds the maximum number between double palindromes for all 1000 offsets of the sequence of trip meters vs full odometers. All of them did find at least two double palindromes and reported the maximum distance apart. The largest of these maxima was 1910, indicating 1909 in a row that were not double maxima, with one double maximum a mile before that interval and one a mile after.

While any setting leads to at least two time seeing a pair of palindromes, there are four possible maximum distances between such pairs given some initial settings:

Depending on the phase relationship between the trip meter and the odometer, any of the below can be the longest distance from one double palindrome and the next:      

      

        1011

        1101

        1111

        1910

        

In each case the number of miles with no such pairing, between those with such a pairing, is 1 less than the distance between pairs.        

An example of the 1910 (with 1909 between) is:

. . .