Sq. 618, the block bounded by N St, New York Ave and 1st St. I see the problem with it, I tried to say too much. That's the problem with the census data and looking at the detailed changes over time, there is just too much. So I decided to switch it up and tell a tale where the info isn't that new to me and I can try to keep the stories simple. Try.
In 1880 there were only 6 people listed as living on the square. There was a carpenter living alone at 305 Q St and the Miller family at 1600 3rd St NW. The Franco-Prussian Miller family interests me (not as much as the 100% German Glorius family on Sq. 519), because the head, John Miller's name is shown as owning most of Sq. 520 and a good portion of Sq. 509E. You can see it on the map shown here, where a tiny bit of the neighboring square is shown. At the time of the 1880 census Mr. Miller had reached the ripe old age of 77, so you can imagine by the 1900 census, he was very, very dead.
There is a thought that this is a place where families put down roots, however, in the case of Sq. 520 (and I believe with many blocks) most people are just passing through. I took the names of everyone from the 1900 to 1940 census and looked for similar names and duplicates across the censuses. There are some people who are found in 2 censuses. Very rare is it to find someone who has managed to stick around for 3 or more with the same address. One of these rarities is Mrs. Mary Davis who lived at 1623 4th St NW from the 1910 to 1930, possibly 1940. Possibly, because the info doesn't match up, as I suspect it may be a same named relative or she was lying about her age. In 1910 she was 38 years old and living with her husband of 13 years, John, mortgage free. There is no change in 1920, except she's 48. By 1930 John is no longer in the picture and she is a widow, working as a matron for the federal government. But here her age changes, she's now 55. By this time she should be 58 years old. In 1940 we have a Mary Davis living at 1623, but she is listed as being 60, when she should be 68 years old. It is not uncommon for a woman to lie about her age.