A031623 Numbers n such that continued fraction for sqrt(n) has odd period and central terms 35.

1226, 15178, 25681, 38537, 52153, 53069, 53993, 70981, 72586, 90289, 91493, 115961, 137341, 140317, 164554, 166993, 168629, 170273, 171098, 192469, 193346, 195989, 196874, 197761, 201329, 229213, 258905, 260941, 262985, 265037, 267097, 271241