The price? Hard to know, real estate agents say, because not since Richard M. Nixon lived in a New York City apartment has the market tried to assess the value of immediate proximity to the president in a dense urban neighborhood. (The Greenwood Avenue neighbors are separated by about 20 feet, a line of thin trees and an iron fence that is more decorative than forbidding.) The Grimshaws paid $35,000 in 1973; other homes in the area have sold for $1 million to $2.5 million.

“We think there’s a premium,” said Matt Garrison, the listing agent with Coldwell Banker, who does not intend to put an asking price on the house. “We don’t know what the Obama effect is.”

Mr. Garrison said he had tried to scout similar parcels of residential property, but pointed out that there was no family living next door to the White House.

“I tried to look at 12 Downing Street, but that’s all offices,” Mr. Garrison said, referring to the building next door to the British prime minister’s residence in London. “Here we are looking out the kitchen window at the president’s back porch. Buyers establish the market. Stuff sells for what people are willing to pay.”

On the third floor, in a playroom, a large picture window offers a sweeping view of the red brick Georgian-style house that Mr. Obama bought in 2005 for $1.65 million.