Briefings are one of Washington's growth industries. Reporters get briefed by anonymous officials. Cabinet members are briefed by their staffs. Senators get briefed behind closed doors. Everyday, President Reagan has an intelligence briefing.

But the longest running briefing in town is the daily (except weekends and holidays) session around noon in the White House press room. And for aficionados, the first briefing of 1982 on Monday was a memorable one.

"When briefings go down in history, I think this one would rank right there at the top," mused briefer Larry Speakes, the principal deputy White House press secretary.

Speakes was being held captive at the rostrum by reporters who would not let the briefing end until they were sure they knew the whereabouts of national security adviser Richard V. Allen.

What had been a routinely uninformative briefing changed when television correspondents learned from reporters staked out at Allen's home that he had left, telling them that he was on his way to the White House to meet Reagan.

"Allen thinks he's going to see the president. That's what he told reporters when he left home," a reporter told Speakes. "Is that right?" Speakes asked back.

Helen Thomas of United Press International, who as the longest-serving wire service reporter has the right to decide when to end a briefing, announced that she would keep this one going until she knew if Allen had arrived.

Speakes asked deputy press secretary Peter Roussel to check. Roussel disappeared and the reporters began stalling for time.

"If we had old Pat Buttram, he could tell a few jokes," Speakes remarked. Buttram, Gene Autry's sidekick, entertained the traveling White House press corps with jokes on New Year's Eve in Palm Springs, Calif.

Instead of cracking jokes, Speakes was asked to read some background information on the Weber case, a Supreme Court decision supporting affirmative action with which Reagan disagrees. Speakes droned on for a couple of minutes, reading the facts of the case, before looking up and asking: "Okay? Anybody listening?"

The dialogue drifted from affirmative action to other topics and back to Allen's whereabouts.

Finally, Roussel reappeared to announce that if Allen was in the White House he was not there to see the president.

The mystery seemed impenetrable until Emery King of NBC announced that his desk had reported that Allen was at a typewriter store on 16th Street NW.

Speakes, seeking light at the end of his tunnel, asked how close the store was to the White House.

He kept saying that at the time he entered the press room, the president was not scheduled to meet with Allen. "Despite all the hullabaloo," he said, "apparently we are right where we were the minute I walked out here."

After 33 minutes, Thomas finally called a halt to the proceedings. An hour and 20 minutes later, Allen met Reagan in the Oval Office and resigned.