Finding the "center integers" of an array

Consider the input vector:

[1 2 3 10 11 12 15 16 17 20 21 22 23 24 30]'

Let's group the elements of the input vector in the following manner:

[1 2 3] [10 11 12] [15 16 17] [20 21 22 23 24] [30] (This is not part of the output)

Then the desired output is the center integer of these "groupings":

[2 11 16 22 30]

Is there a quick and easy way to do this with only a few functions? (Preferably without a for-loop). Let's assume these integer "groupings" contain an odd number of elements so there is always one center integer.

I have no starting code unfortunately. I considered using the diff command, but I got stuck from there.

Let me know if I need to clarify anything. Thank you for your help.

Answer 1

[Walter Roberson]

t = find([true, diff(X)>1, true]);
Output = X((t(1:end-1) + t(2:end)-1)/2);

Answer 2

[Alfonso Nieto-Castanon]

 x = [1 2 3 10 11 12 15 16 17 20 21 22 23 24 30];
 y = x(floor(convn(find(diff([nan x nan])~=1),[1 1]/2,'valid')));

Answer 3

[Alfonso Nieto-Castanon]

 x = [1 2 3 10 11 12 15 16 17 20 21 22 23 24 30];
 y = cellfun(@mean,mat2cell(x, 1, diff(find(diff([nan x nan])~=1))));