Pair sequence number is a the output of a program made by BashicuHyudora and posted at a googology-related thread of the Japanese site BBS 2ch.net in 2014. The algorithm of the program is called the pair sequence system, a weak version of Bashicu's matrix system by the same creator. It is supposed to calculate number comparable to \(f_{\vartheta(\Omega_\omega)+1}(10)\). It is an extension of a system named the primitive sequence system, still by the same author, which generates a number approaching \(f_{\varepsilon_0+1}(10)\).