nat(0).
nat(X) :- nat(Y), X is Y + 1.

ar_prog([H|T]) :- nat(S), genKS([H, Diff, L], 3, S), ar_prog_helper([H|T], Diff, L).

ar_prog_helper([], _, 0).
ar_prog_helper([X], _, 1).
ar_prog_helper([H1,H2|T], Diff, L) :- L > 1, L1 is L - 1, H2 is H1 + Diff, ar_prog_helper([H2|T], Diff, L1).