According to the second edition of Alan Lawrie's Saturn ("the complete Saturn V manufacturing and test records") 98 production F-1 engines, 82 development engines, seven serialized mock-ups, and a shop floor engineering model were manufactured by Rocketdyne.

While rummaging around in the Young Collection in the UAH archives I came across a modern-looking computer print-out of F-1 rocket engine serial numbers. Handwritten notes on the sheet of paper indicated that it was dated "7-19-94" and that it was "from Bob Biggs computer database" (Bob Biggs was a Rocketdyne engineer who worked on F-1 and SSME, authoring the F-1 chapter of Remembering the Giants: Apollo Rocket Propulsion Development and "Space Shuttle Main Engine: The First Ten Years"). The handwriting also noted that there were a total of 183 engines.

F-1 Engines

F001	F2007	F025-2	F2057	F2085
F002	F2003	F030	F035	F2086
F001-0	F2009	F028-1	F2058	F108-2
F004	F024	F2030	F2059	F2087
F004-0	F2010	F031	F2060	F2088
F005	F020-1	F2031	F2061	F110-1
F002-0	F2011	F2032	F102-2	F2090
F005-0	F2012	F026-2	F2063	F109-4
F007	F2013	F2033	F2062	F2089
F008	F025	F2034	F2064	F2091
F006-1	F013-2	F027-2	F2065	F040
F003	F2014	F2035	F103-1	F2092
F009	F014-1	F2036	F2038-1	F2093
F010	F2015	F2037	F2009-1	F2094
F009-1	F2016	F2038	F2066	F112-1
F008-1	F023-1	F032	F036	F2095
F009-2	F2017	F2039	F2067	F2096
F011	F026	F2040	F2068	F111-3
F012	F027	F029-1	F104-4	F2097
F010-1	F2018	F2041	F2069	F2098
F006-2	F020-2	F033	F2070	F113-2
F010-2	F2019	F2042	F2071	F041
F013	F025-1	F025-3	F2072	F110.1
F1001	F2020	F2043	F2073
F011-1	F2021	F2044	F2074
F1002	F028	F2045	F2075
F014	F3T1	F030-1	F105-1
F018	F2022	F2046	F2076
F019	F2023	F2047	F2077
F020	F026-1	F2048	F2079
F012-1	F2024	F2049	F037
F021	F4T2	F2050	F2078
F011-2	F027-1	F2051	F2080
F022	F2025	F2052	F2081
F013-1	F029	F2053	F106-3
F2004	F2026	F034	F038
F023	F2027	F2054	F2082
F2005	F2028	F2055	F107-1
F2006	F020-3	F101-2	F2083
F2008	F2029	F2056	F2084

This list uses Rocketdyne's internal serial number scheme, which differed from the one used by NASA in that the first digit was not incremented to indicate different blocks of production engines (other than changing from the F1xxx series to the F2xxx series; the F1xxx configuration block consisted of only two engines which were built and delivered for ground test while the F2xxx series included engines intended for flight vehicles).

Engines other than those of the form "F1xxx" or "F2xxx" represent R&D engines. Lawrie notes that F3T1 and F4T2 were "manufactured by NASA as a learning exercise using spare parts."

Since the list is not strictly in either numeric or "ASCIIbetical order", it's possible that the serial numbers are listed in the order in which the engines were manufactured. However, this is pure speculation on my part.

It's hard to decipher how, exactly, engines are counted. Lawrie cites 180 engines (98 production plus 82 development engines) while the list above tallies 183 entries.

As Lawrie notes in his book, many engines were rebuilt at various stages, resulting in a dash number after the main serial number. This list contains 46 such engines (leaving 137 main engine serial numbers). However, there are also many engines (F006-1, F006-2, F101-2, F102-2, F103-1, F104-4, F105-1, F106-3, F107-1, F108-2, F109-4, F110-1, F110.1, F111-3, F112-1, F113-2) which have a dash number but no corresponding main serial number in this list. In several cases (F101-2, F102-2, F104-4, F106-3, F108-2, F109-4, F111-3, F113-2), not only is the main serial number missing, but so are the preceding dash numbers. For example, in the case of "F104-4" there is no F104, F104-1, F104-2, or F-104-3, leaving four engines accounted for. When removing any serial number modifiers (the dash number or, in the case of F110.1, the "dot number"), there are 150 distinct engines.

Lawrie's book also documents a number of surviving engines whose engines contain a dash number (F2038-2, F2045-1, F114-2) which do not appear in the list above. For the two production engines, F2038, F2038-1, and F2045 do appear in Biggs' list, but neither the base F114 nor F114-1 R&D engines appear above.

Sadly, a complete and accurate list of engine serial numbers and the criteria for what counts as an "engine" may be lost to history, but this is the most complete list of F-1 serial numbers I've seen.

Text-searchable PDF of the computer printout: F-1 Rocket Engine Serial Numbers