Hyperdimensional computing (HDC), also known as vector symbolic architectures (VSA), is a computing framework used within artificial intelligence and cognitive computing that operates with distributed vector representations of large fixed dimensionality. A critical step in designing the HDC/VSA solutions is to obtain such representations from the input data. Here, we focus on a wide-spread data type of sequences and propose their transformation to distributed representations that both preserve the similarity of identical sequence elements at nearby positions and are equivariant with respect to the sequence shift. These properties are enabled by forming representations of sequence positions using recursive binding as well as superposition operations. The proposed transformation was experimentally investigated with symbolic strings used for modeling human perception of word similarity. The obtained results are on a par with more sophisticated approaches from the literature. The proposed transformation was designed for the HDC/VSA model known as Fourier Holographic Reduced Representations. However, it can be adapted to some other HDC/VSA models.