This prints the first field and then every subsequent field until end of the line.
$ awk '{for (i=2;i<=NF;i++) print $1,$i}' file P04637 1A1U P04637 1AIE P04637 1C26 P04637 1DT7 P04637 1GZH P04637 1H26 P04637 1HS5 P04637 1JSP P04637 1KZY P04637 1MA3 P04637 1OLG P04637 1OLH P04637 1PES P04637 1PET P04637 1SAE P04637 1SAF P04637 1SAK P04637 1SAL P04637 1TSR P04637 1TUP P04637 1UOL P04637 1XQH P04637 1YC5 P04637 1YCQ
To get exactly what OP request, no more, no less:
awk '{print $1,$2 RS $1,$4 RS $1,$3 RS $1,$5 RS $1,$23 RS $1,$11 RS $1,$14 RS $1,$16}' file P04637 1A1U P04637 1C26 P04637 1AIE P04637 1DT7 P04637 1XQH P04637 1MA3 P04637 1PES P04637 1SAE