A031575 Numbers n such that continued fraction for sqrt(n) has even period and central term 77.

5931, 5939, 5987, 5999, 6007, 6011, 6043, 6047, 6059, 6067, 6079, 6091, 6103, 6131, 6143, 6151, 6163, 6167, 6171, 6191, 6199, 6203, 6211, 6219, 6223, 6239, 23720, 23808, 23816, 23840, 23872, 23904, 23936, 24008, 24040, 24064, 24128, 24192, 24224, 24256