[By all accounts, Timothy Caughman was a benevolent man content with an unassuming life, living in a former single room occupancy residence that had been his longtime home. For more about his life, read here.]

Twenty-five hours later, Mr. Jackson, who had seen his image from surveillance video in news reports, walked into the police substation in Times Square and told officers to arrest him, the police said. He was taken to the same precinct where Mr. Caughman had sought help.

Mr. Jackson spent about two hours talking to detectives, prosecutors said. They showed about an hour of the interview on Thursday, and planned to show the rest on Friday.

“I was going for something a bit bigger,” Mr. Jackson told his interrogators, explaining that over the course of several days in New York, with a hotel in Times Square as his base, he walked around Manhattan actively stalking between 10 and 15 individuals or groups with the thought of killing them. He said he almost carried out other attacks, using two knives hidden in his pockets, but hesitated.

“It’s more complicated than you think,” he said.

[Mayor Bill de Blasio spoke at the funeral of Timothy Caughman, who was remembered as a individual of quiet dignity and broad interests. Read more here.]

He said he felt “kind of bad” that his victim was an older man — but only because he wanted to kill somebody younger. When Detective Barbara asked him if he felt any remorse, Mr. Jackson said, “No,” adding, “He’s a homeless black guy.”

Mr. Jackson said his next step was to move on to a larger attack in a city that he called the center of the media universe. “I wanted to basically influence the national conversation,” he said.