A031586 Numbers n such that continued fraction for sqrt(n) has even period and central term 88.

7746, 7778, 7782, 7814, 7822, 7838, 7842, 7846, 7862, 7874, 7886, 7894, 7906, 7934, 7954, 7974, 7986, 8002, 8006, 8014, 8018, 8038, 8054, 8078, 8098, 17427, 17463, 17481, 17499, 17502, 17508, 17517, 17529, 17553, 17601, 17607, 17637, 17652, 17709