A031420 Numbers n such that continued fraction for sqrt(n) has odd period and central terms 7.

50, 349, 778, 1105, 1237, 1306, 1565, 1721, 2473, 3361, 3706, 3889, 4133, 4985, 5261, 5545, 6217, 6841, 6929, 7165, 7253, 7418, 7754, 8021, 8273, 8369, 8629, 9089, 9274, 9461, 10034, 10229, 10333, 10729, 11245, 11657, 12077, 12842