But Mr. Bloomberg is not one to act rashly. He started his hunt in 2001, but it wasn’t until 2010 that he settled on Riverside Drive, across the street from Joan of Arc Park, where he used to play football. The 2,175-square-foot apartment in a 1902 building designed by Ralph S. Townsend overlooks the Hudson, has 11-foot ceilings and the details that Mr. Bloomberg was looking for.

“I am very particular. It took three years to renovate. It didn’t even need a renovation,” he said. It took another two years to sell his house on Lake Winnipesaukee in New Hampshire, delaying his return to the city until this spring.

Mr. Bloomberg was ready to make the transition, to be less sedentary and more engaged in city life. “Over the decades, I’ve lost touch with just about everybody,” he said before he arrived in early May. “I look forward to having a big dinner party with them in my new apartment. It will be great fun, though we are no longer young men.”

Upon moving in, however, the anticipation turned rapidly to upset. Mr. Bloomberg walked into and out of five supermarkets, unable to navigate the narrow aisles. His phone wouldn’t work. His television and computer wouldn’t turn on. He was dismayed to see litter.

After four days in the city, he thought to himself: “I can no longer cope. I don’t think I can possibly live here again.” Now, some weeks later, Mr. Bloomberg is still here, though still out of sorts. He contemplated selling the apartment and leaving — where to, he was not sure — but the expense of such a turnaround dissuaded him. He did secure a New York City phone number. Adaptation, could it be?

Expectations vary, according to Jeff Feuer, an associate broker with Douglas Elliman Real Estate and Mr. Bloomberg’s real estate agent for 10 years. Typically, he said, the adjustment is a lot more difficult if you are leaving New York than if you are returning.

“I have a house in Woodstock, and I love it,” he said, “but even after a couple of days, I just want to come back.”