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Single image super-resolution (SR) has long posed a challenge in the field of computer vision. While the advent of deep learning has led to the emergence of numerous methods aimed at tackling this persistent issue, the current methodologies still encounter challenges in modeling long sequence information, leading to limitations in effectively capturing the global pixel interactions. To tackle this challenge and achieve superior SR outcomes, we propose the Mamba pixel-wise sequential interaction network (MPSI), aimed at enhancing the establishment of long-range connections of information, particularly focusing on pixel-wise sequential interaction. We propose the Channel-Mamba Block (CMB) to capture comprehensive pixel interaction information by effectively modeling long sequence information. Moreover, in the existing SR methodologies, there persists the issue of the neglect of features extracted by preceding layers, leading to the loss of valuable feature information. While certain existing models strive to preserve these features, they frequently encounter difficulty in establishing connections across all layers. To overcome this limitation, MPSI introduces the Mamba channel recursion module (MCRM), which maximizes the retention of valuable feature information from early layers, thereby facilitating the acquisition of pixel sequence interaction information from multiple-level layers. Through extensive experimentation, we demonstrate that MPSI outperforms existing super-resolution methods in terms of image reconstruction results, attaining state-of-the-art performance.