A051261 Main diagonal of A018219, i.e. (n,n,a_n) is a winning position.

0, 4, 6, 1, 3, 7, 11, 2, 5, 10, 17, 23, 21, 9, 28, 26, 24, 8, 34, 12, 35, 13, 32, 29, 44, 19, 45, 15, 18, 14, 57, 56, 16, 20, 58, 48, 25, 54, 73, 76, 72, 27, 75, 82, 62, 66, 84, 87, 71, 78, 95, 31, 74, 94, 97, 103, 22, 40, 39, 30, 86, 33, 41, 91, 46, 42, 117, 119, 122, 37