A031553 that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 55.

3027, 3031, 3051, 3067, 3079, 3083, 3091, 3099, 3119, 3139, 3147, 3151, 3163, 3167, 3179, 3187, 3191, 3203, 3239, 3247, 12104, 12128, 12160, 12192, 12200, 12288, 12296, 12384, 12392, 12416, 12448, 12480, 12520, 12608, 12672, 12680, 12704, 12776, 12800