Josephus problem (counting out)

Minsky Register Machine (25 non-halt states)

Not technically a function, but it's in a computing paradigm which doesn't have functions per se...

This is a slight variation on the main test case of my first MRM interpretation challenge:

Input in registers n and k; output in register r; it is assumed that r=i=t=0 on entry. The first two halt instructions are error cases.

Python, 36

I also used the formula from wikipedia:

J=lambda n,k:n<2or(J(n-1,k)+k-1)%n+1

Examples:

>>> J(7,3)
4
>>> J(77,8)
1
>>> J(123,12)
21

Mathematica, 38 36 bytes

Same Wikipedia formula:

1~f~_=1
n_~f~k_:=Mod[f[n-1,k]+k,n,1]