# Problem 167: Investigating Ulam sequences
For two positive integers a and b, the Ulam sequence U(a,b) is defined
by U(a,b)1 = a, U(a,b)2 = b and for k > 2, U(a,b)k is the smallest
integer greater than U(a,b)(k-1) which can be written in exactly one way
as the sum of two distinct previous members of U(a,b). For example, the
sequence U(1,2) begins with 1, 2, 3 = 1 + 2, 4 = 1 + 3, 6 = 2 + 4, 8 = 2
+ 6, 11 = 3 + 8; 5 does not belong to it because 5 = 1 + 4 = 2 + 3 has
two representations as the sum of two previous members, likewise 7 = 1 +
6 = 3 + 4. Find ∑U(2,2n+1)k for 2 ≤ n ≤10, where k = 1011.