A105829 For n>2, a(n) not appeared previously is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=4.

1, 4, 5, 6, 8, 14, 9, 18, 7, 11, 30, 41, 15, 26, 21, 17, 38, 39, 27, 12, 20, 13, 33, 46, 19, 2, 72, 74, 23, 51, 54, 96, 24, 36, 60, 56, 32, 78, 47, 10, 37, 65, 102, 167, 67, 100, 68, 59, 105, 164, 45, 119, 48, 71, 29, 42, 135, 132, 3, 129, 270, 351, 66, 40, 64, 90, 61, 53, 114