Federal authorities are becoming increasingly persuaded that John W. Hinckley Jr., the man accused of shooting President Reagan, stalked President Carter earlier and would have been satisfied with either man as the target of his "historical deed."

The indications mounted yesterdeay with reports that Hinckley was registered at a Dayton, Ohio, hotel Oct. 2 when Carter landed in the city for a town hall-style campaign appearance in the Dayton Convention Center a block away.

The Dayton Daily News said in a copyrighted story that Hinckley registered at the Sheraton Dayton Hotel Sept. 30 under his own name and stayed in an eight-floor room overlooking the convention center.

Sources say the FBI has also established that Hinckley was in Washington in late September, apparently after he had bought three handguns at some pawnshops in Lubbock, Tex.

A witness reportedly indentified Hinckley as having been near the Capitol. This was presumably shortly before the trip to Dayton.

FBI officials refused to confirm or deny the Dayton visit. The Dayton Daily News said, however, that the FBI traced Hinckley there because he had cashed several travelers' checks in the Ohio city, including two at the Sheraton Dayton.

The newspaper said a hotel employe identified Hinckley from a photograph. He was said to have checked out Oct. 2, the day Carter held the 22nd town hall meeting of his presidency.

Hinckley also spent some time in Chicago Oct. 6 and Oct. 7 at the mid-point of the campaign. Carter plumped for votes in the Chicago area Oct. 6, starting the day in a suburban township and winding up at a Democratic fund-raising dinner that night.

From Chicago, Hinckley flew to Nashville, checking into the Opryland Hotel near the airport terminal on the evening of Oct. 7. He moved to the Downtowner Hotel the next day, perhaps because it was less expensive.

The morning after that, Oct. 9, Carter arrived in Nashville aboard Air Force One for another campaign appearance, this one a fund-raiser at the Opryland Hotel. Around the same time, reportedly about 11 a.m., Hinkley checked out of the Downtowner.

He was arrested at the airport about two hours later when he rushed to catch a flight to New York, too late to check his luggage through.An X-ray check of his hand-carried baggage led to the discovery of three handguns, a box of hollow-point bullets and a pair of handcuffs.

Released several hours later, Hinckley caught a late afternoon flight to New York. Carter was scheduled to be there on Oct. 13 and Oct. 16. Reagan was expected in New York Oct. 16. But by the 13th, Hinckley was back in Texas, buying two more handguns at a Dallas Pawnshop.

A Dec. 10 clipping from The Washington Post, found in Hinckley's hotel room after his arrest here last month, suggested he may have been in the capital again before Carter left office, but investigators apparently are not yet satisfied of that.

The FBI, searching Hinckley's hotel room after the March 30 shooting, found an unmailed letter to actress Jodie Foster in which Hinckley described his plan to "get Reagan" as a "historical deed" that he hoped would gain her "respect and love."

Sources familiar with the investigation say, however, all indications at present suggest that "any president" could have been the target.

"I don't think this guy had a grudge against Reagan," said one. "If you take all the circumstances -- such as Nashville -- Jodie Foster, this guy didn't care how he did it, he was just going to do something monumental."