Hi Keroppi . . .

I am with a Beater: 3836848 is a head casting number first used in '56 on a 235.

I have a feeling that the serial number on your particular block was transferred there from another engine. Back in the day there were several states where Titles and Bills-of-Sale carried the engine serial number as the vehicle identification. So when this newer engine was swapped into the vehicle the old number was transferred in order to jibe with the paper work on the vehicle.

But the number you have is somewhat confusing because AFAIK that two letter prefix was never used. 1946 was the transition year away from two letter prefix to YAP codes (Year Application Plant):
Old Car Manual Project
Early '46 trucks had engine codes of BG and BL which was a carry over from '42. The second series had engine codes of DAA and DAM. This is for the light (1/2 ton) trucks that had 'car' engines.

Alot of serial number listings on the internet just summarize all of the prefixes by year. If one goes back to the original Specifications Guide one can find the 'Application' codes for the heavier and long wheel base trucks:
tocmp: 1946 Truck Specifications

So a BM is a 216ci truck engine for a 3100 series built in Tonawanda. But the Year is missing . . . e.g. DBM - '46, EBM - '47 , FBM - '48 etc.

When the engine serial was transferred it was omitted. Perhaps because it was also omitted on the Title? Speculation but plausible.

Moreover the YAP numbering scheme only runs through '53. In '54 the codes changed and moved to a suffix (as described at the Old Car Manual Project).

So in this case - casting numbers are all we can go one.

regards,
stock49

Update: I did a little more leg work over the GM Heritage Center. I was curious about this BM prefix. That prefix was actually used in '42 on 3/4 ton heavy duty optioned trucks: 1942 Specifications - serial numbers are on page 6.