A029946 a(n)^3 contains n-th prime as a substring.

3, 7, 5, 3, 45, 11, 12, 13, 47, 9, 11, 15, 81, 7, 63, 37, 19, 21, 23, 83, 46, 31, 18, 29, 13, 106, 47, 221, 103, 225, 238, 236, 255, 225, 285, 205, 54, 168, 23, 161, 148, 122, 106, 57, 13, 271, 171, 247, 497, 132, 177, 198, 148, 136, 137, 133, 61, 358