Information from the US censuses is being posted here to try to give us all more information than you have posted.
Did Jacob's American marriage record, wedding in a church record or even obituary give any information about his father's name? Patronymic naming in Norway at that time makes that very vital information.
The US censuses for Miner Co. SD indicate that Jacob married twice - so you have twice the chance of finding some listing of his father's given name.
In the 1920 census he is listed as Jacob J. Holm -- the J. can be important clue to his father's name.