President Barack Obama shares a laugh with David Letterman during a break at a taping of “The Late Show with David Letterman” on Monday at the Ed Sullivan Theater in New York.

New York ? Add this one to the presidential collection: the heart-shaped potato.

By the time Barack Obama came on stage to the taping of the “Late Show” on Monday, host David Letterman had offered up 10 reasons why in the world the president had agreed to do it.

Among Letterman’s theories: Obama said yes without thinking about it, or as Letterman put it, “Like Bush did with Iraq.”

But Obama had other ideas. It turns out he was listening when Letterman had bantered with a woman in the audience who brought — yes — a potato in the shape of a heart to the show.

Obama told Letterman: “The main reason I’m here? I want to see that heart-shaped potato.”

The woman tossed the potato to Letterman.

She agreed to let Obama keep it. Said the president: “This is remarkable.”

Obama also had his most irreverent answer yet on the question of whether some of the vitriolic reaction to his health care plan is driven at least partly by racism.

“First of all, I think it’s important to realize that I was actually black before the election,” Obama said to huge laughs from Letterman and the audience.

Responded Letterman: “How long have you been a black man?”

Letterman covered a number of topics with Obama — many of them serious — in a taping that ran about 40 minutes. The show will be broadcast on CBS on Monday evening.

On the economy, Obama offered a sober prediction as the country deals with 9.7 percent unemployment, the worst level since 1983. He said he expects unemployment will be a “big problem” for at least another year. But he also said the economy will rebound even stronger.

As for the war in Afghanistan, Obama said he won’t make a decision on sending in more troops, until he completes a comprehensive review of the war effort and settles on his next strategy.

“I’m going to be asking some very hard questions,” Obama said.

Obama’s visit made him the first sitting president to appear on Letterman’s program. He had been on Letterman’s show five times before, though, most recently in September 2008.