Selected Mapping (SLM) technique is one of the promising PAPR reduction techniques for Orthogonal Frequency Division Multiplexing (OFDM). But this reduction technique results in a huge amount of computation complexity which is costly and time consuming. In this paper, Riemann sequences are used as a phase vectors along with the thresholding of the power amplifier(PA). The default index of the phase sequence is used to reduce the computational complexity of SLM technique. The default index of a phase sequence refers to the starting index for the phase vectors in the SLM scheme. This index is derived from the experimentation results. The Matlab simulations show that the complexity has been reduced by 98 percent if the threshold value of PA is around 3.0dB.