A053803 Numbers where the difference of consecutive cubes is "close" to another cube: let A = x^3 - (x-1)^3, sequence is the x's where A - int(A^(1/3))^3 < int(x^(1/2))^3.

1, 7, 9, 19, 22, 25, 28, 31, 38, 41, 45, 49, 53, 57, 61, 65, 69, 73, 78, 82, 87, 91, 92, 96, 101, 106, 110, 111, 115, 116, 121, 126, 131, 132, 136, 137, 142, 147, 148, 153, 158, 159, 164, 165, 170, 171, 175, 176, 181, 182, 187, 188, 193, 194, 199, 200, 205, 206