A065337 a(n) is the smallest number not already used such that Sum_{m = 0 .. n-1} a(m)*a(m+1) is a square.

1, 4, 3, 11, 16, 19, 33, 21, 31, 96, 13, 65, 63, 55, 145, 336, 40, 240, 53, 429, 272, 376, 130, 380, 108, 78, 1368, 49, 235, 288, 196, 627, 59, 1360, 52, 738, 192, 312, 75, 157, 2432, 81, 313, 3040, 209, 603, 1120, 45, 281, 4448, 2847, 357, 1265, 784, 1153, 9495