I have a copy of P.Duffett-Smith's "Practical Astronomy with your Calculator", 2nd edition, and here is his precession algorithm where a1, d1 are the precessed Right Ascension and Declination and a0, d0 are the original right ascension and declination, respectively. The Nautical Almanac will show you how to convert from Right Ascension to Sidereal Hour Angle.
a1 = a0 + (m + n sin a0 tan d0) x N
d1 = d0 + (n' cos a0) X N
where N is the number of years elapsed since the Epoch. The Epoch is the base date from which the star positions in your star catalog are plotted to. Most modern sources are plotted to Epoch 2000.0, The Nautical Almanac is published every year with all positions already reduced to the current Epoch. In fact, that's why they publish a new one every year! So for example, this year's Almanac has all positions plotted for the Epoch at the moment they are looked up for, so you don't need to precess at all.
The constants m, n and n' for Epoch 2000.0 are 3.07420 sec, 1.33589 sec and 20.0383 arcsec, respectively.
Here are the constants for m, n and n', respectively, for some other common Epochs.
Epoch 1900.0 --- 3.07234, 1.33646, 20.0468
Epoch 1950.0 --- 3.07327, 1.33617, 20.0426
Epoch 1975.0 --- 3.07374, 1.33603, 20.0405
You can interpolate these values for "Epochs" falling on other dates.
This is considered an approximate formula, but is probably accurate enough for celestial navigation purposes for dates within our lifetime.
That's all I'm interested in. For navigation there is no sense predicting where to look for stars beyond our lifetime.
BTW, please don't think I'm trying to impress you guys by throwing all this stuff at you, I majored in astronomy in college, and I still do it as a hobby, so it was and is my job to know all this math. I'm sure every one of you guys knows things and does stuff at work every day that I would be helpless with. I for example, need my wife to program my TV to record a show I want to watch later, and it once took me a whole day to figure out how to re-pack a boat trailer bearing even with the instructions right in front of me. On the other hand, the Navy taught me how to field-strip and reassemble a .45 Auto blindfolded. Believe me, once you know how to do something, it is never as hard as it looks. It's learning that is hard, not doing.
Thanks for posting this. Maybe this level of detail is marginally off topic but I find your astronomy posts interesting. Having not majored in astronomy I've not quite been able to "crack the code" that you astronomer speak in.
Curtis
