User blog:QuasarBooster/FC0 greedy lists

A greedy list L is an ordered tuple x_1,x_2,x_3,...,x_n of natural numbers (i.e. n>=0) where x_n != 0. To obtain a value from this list, denoted as v(L), consider another tuple y_1,y_2,y_3,...,y_n where, for each i:

if i = n: y_i = - 1 if i = 1 or if x_i = 0: y_i = x_n otherwise: y_i = v(L') where L' is a copy of L with x_i decreased by 1

Then, v(L) = v(x_1+y_1,x_2+y_2,x_3+y_3,...,x_n+y_n). Additionally, v(x_1,x_2,...,x_(n-1),0) = v(x_1,x_2,...,x_(n-1)) v(x_1) = x_1.

I'm not proud of this explanation but hopefully it suffices. I'll define the function gL(n) = v(n,n,n,...,n). (I.e. the value of an n-tuple where each entry is n.)