I've formulated actual algorithms that compute the so-called hyperbasveo functions. Their "definitions" can be found here:
http://www.topix.net/forum/science/mathematics/TQO3VIEVJSF8IKTOE

Note that there is a problem with his definition - you can't define n as an input parameter, and then say "for n = 1...10." Either it's a parameter or it isn't. I've gone ahead and stubstituted nmax instead of n.

Basveo[b_, nmax_, a_] := 
      Module[{k, n, list}, 
list = 
          Range[nmax]; 
For[n = 1, 
          n ≤ 10, n++, 
k = 
            Mod[n, b]; 
If[Mod[k, 2] ≠ 0, 
            list[[n]] = 
              n + a];
]; 
list
]

Basveo[3, 10, 10]

Notice that there is exactly one minor difference between Basveo and openBasveo, where the modulus m is subustituted for the modulus 2.

OpenBasveo[m_, b_, nmax_, a_] := 
      Module[{k, list}, 
list = 
          Range[nmax]; 
For[n = 1, 
          n ≤ 10, n++, 
k = 
            Mod[n, b]; 
If[Mod[k, m] ≠ 0, 
            list[[n]] = 
              n + a];
]; 
list
]

OpenBasveo[2, 10, 10, 10]
OpenBasveo[3, 9, 10, 5]

Notice that here we just change the bounds on n. For that reason, nmax is no longer a parameter:

HyperBasveo[s_, t_, m_, b_, a_] := 
      Module[{n, k, list}, 
list = 
          Range[s, t]; 
For[n = s, 
          n ≤ t, n++, 
k = 
            Mod[n, b]; 
If[Mod[k, m] ≠ 0, 
            list[[n - s + 1]] = 
              n + a];
]; 
list
]

HyperBasveo[1, 10, 2, 10, 10]
HyperBasveo[1, 10, 3, 9, 5]
HyperBasveo[3, 8, 2, 7, 8]

Now he asks us to set:
function(n)= HyperBasveo(n+1,1,n+1,i,n+1,n+ 1) - PrimeNumber(Nth)
Which actually wants the n + (1^st) element of one of our properly-written HyperBasveo functions. He has substituted his counter i instead of n because n has been reused. We discard that undefined (and irrelevant) "parameter."

f1[n_] := 
        HyperBasveo[1, n + 1, n + 1, n + 1, 
          n + 1];
f2[n_] := f1[n][[n + 1]]
f[n_] := f2[n] - Prime[n]

Table[f1[n], {n, 1, 10}] // TableForm
Table[f2[n], {n, 1, 10}]
Table[f[n], {n, 1, 10}]

It appears that none of this is very meaningful.