Specific function

[onako]

For determination of the distance from a certain point, a function should be used. Namely, the input values 'x' are from N (1,2,3,4,5...), and the corresponding outputs 'y' from R, but such that the sequence 'y' (relative to 'x') is increasing;
$y(1)<y(2)<y(3)<y(4)<...$ \\
but to satisfy \\
$y(1)>[y(2)-y(1)]>[y(3)-y(2)]>[y(4)-y(3)]>...$
The function that satisfies this is sqrt(x), but I'm interested in other possible functions that satisfy the above. The 'derivatives' of sqrt(x) should also work.

Thanks