In 1920 Ole and Martin Anderson were living in Virginia, Union, SD and were farmers.
In 1935 Ole was living in the same place and then in 1940 he was in the County Poor Farm.
Ole A. Anderson
Died: 6 Dec 1941, Union Co. SD
Death Index 1879-1955
For what it's worth, I'd say it's the same Ole Anderson especially since no other Ole Anderson died in that county in that time frame.
You can contact the Union County Historical Society, www.facebook.com/unioncountyhistoricalsociety/about/
and ask if they can provide a copy of his obituary or if the local public library can do so.
You might have to contact the State Archives/S.D. State Historical Society, www.history.sd.gov/archives/
I'd also contact the State Archives/S.D. State Historical Society for the Poor Farm records. Sometimes you can find them in tact at that kind of organization. Generally the records don't exist. Successful Searching!