Getting the mfgr date on a 141 is easier to do using the Remington Date Code on the left side of the bbl. I don't know of any serialnumber chart for them, but some collectors can usually tell rather quickly by experience.
The date code is a 2 or 3 letter stamping.
The month is coded out in the word 'BLACKPOWDERX'
12 letters,,12 months. B-January,,L-February,,A-March,,ect to X-December.
Then a one or two letter code for the year of mfg'r.
This code system started in 1921 and the letter M
M-1921
N-1922
Letter 'O' is skipped here (but used later).
P- 1923
Letter Q is skipped
R-1924
and on and on...
....date code 'LR' would be Feb. 1924
When the yr code came around to M again,,they simply doubled it to 'MM' and continued doubling the letter code to ZZ in '53. Then they started again with the letter 'A'.
So there are a few duplicates,,but knowing the model and era of the gun you have in hand,it's easy enough to figure out the mfg'r date code.
There may also be a 'Repair code' stamped on the left side. Another date code w/a '3' in it. Rifle returned and repaired. There's others (Canadian Export, No work done,returned, ,,,) each will have a different number in with a date code.
Date codes are all letters.
Here's a link to the Remington date codes. Confusing at first,but really quite simple. Used right up to acouple years ago.
Remington Society of America - questions/barrelcodes
The date code being on the bbl sometimes brings up thepossibility of a switched bbl and a wrong mfg;r date code. That is much more often to happen on one of their shotguns with their easily TD bbls.
Check other features on the gun especially the sights on the rifle.
I don't recall if the 14/141 bbls were serial numbered and if so in plain sight.
It may be underneath the mag tube action slide and tough to see w/o taking things apart