We propose an approximation of echo state networks (ESNs) that can be efficiently implemented on digital hardware based on the mathematics of hyperdimensional computing. The reservoir of the proposed integer ESN (intESN) is a vector containing only n-bits integers (where n< 8 is normally sufficient for a satisfactory performance). The recurrent matrix multiplication is replaced with an efficient cyclic shift operation. The proposed intESN approach is verified with typical tasks in reservoir computing: memorizing of a sequence of inputs, classifying time series, and learning dynamic processes. Such architecture results in dramatic improvements in memory footprint and computational efficiency, with minimal performance loss. The experiments on a field-programmable gate array confirm that the proposed intESN approach is much more energy efficient than the conventional ESN.