
EXAMPLE

For n=1, let the ordered sequence of integers be S = (s_1). The maximum value of the Gilbreath equation of S is k = s_1 + 1. Rewriting this as a function of s_1 gives s_1 + 1, which can take only 1 value, so a(1)=1.
For n=2, let the ordered sequence of integers be S = (s_1, s_2). The maximum value of the Gilbreath equation of S is k = s_1^1 + s2 + 1. Rewriting this as a function of s_1, s_2 gives 1  s_1 + 2*s_2, which can take only 1 value, so a(2)=1.
For n=3, let the ordered sequence of integers be S = (s_1, s_2, s_3). The maximum value of the Gilbreath equation of S is k = s_1^2 + s_2^1 + s_3 + 1. Rewriting this as a function of s_1, s_2, s_3 gives 1  s_2 + 2*s_3 + s_1  2*s_2 + s_3, which can take 2 distinct values, so a(3)=2.
