A046838 Numbers n such that n^2 can be obtained from n by inserting a block of digits.

0, 1, 5, 6, 10, 11, 25, 76, 95, 96, 100, 101, 125, 376, 625, 976, 995, 996, 1000, 1001, 1025, 1376, 9376, 9625, 9976, 9995, 9996, 10000, 10001, 10025, 10376, 10625, 90625, 99376, 99625, 99976, 99995, 99996, 100000, 100001, 100025, 100376