Here is one way of doing it:
A=[1,1;
1,2;
1,3;
2,4;
2,5;
2,6;
3,7;
3,8;
3,9;
2,10;
2,11;
2,12;
1,13;
1,14;
1,15;]
runlengths = diff([0; find(diff(A(:, 1))); size(A, 1)]); %find length of each run of consecutive numbers
rowids = repelem((1:numel(runlengths))', runlengths); %assign unique ids to each run
[A(cumsum(runlengths), 1), accumarray(rowids, A(:, 2), [], @min)] %use accumarray to find the minimum per rowid
