The nth Monica set M_n is defined as the set of composite numbers x for which n|[S(x) - S_p(x)], where x | = | a_0 + a_1(10^1) + ... + a_d(10^d) | = | p_1 p_2 ...p_m, and S(x) | = | sum_(j = 0)^d a_j S_p(x) | = | sum_(i = 1)^m S(p_i). Every Monica set has an infinite number of elements. The Monica set M_n is a superset of the Suzanne set S_n.

Smith number | Suzanne set