He enjoyed a home-cooked dinner in Montana with a former U.S. senator. He visited Telluride, Colo., and Moab, Utah, a vacation spot known for its national parks. And he chatted about start-ups with Sam Altman, the chief executive of OpenAI.

After pleading guilty to a money-laundering violation in November, Changpeng Zhao, the founder of the cryptocurrency exchange Binance, did not sit still. A federal judge denied his request to return home to Dubai, but Mr. Zhao, 47, was free to roam the United States. So he spent the past five months traveling the country, networking with other entrepreneurs and laying the groundwork for his next act.

When he pleaded guilty, Mr. Zhao, once the most powerful figure in the global crypto industry, resigned as Binance’s chief executive and agreed to pay a $50 million fine. On Tuesday, a federal judge in Seattle sentenced him to four months in prison; prosecutors had sought a three-year prison term, while defense lawyers had asked for probation and no time behind bars.

But Mr. Zhao, who goes by the initials CZ, is already looking to the future. He has a $33 billion fortune, according to Forbes, and he announced last month that he was starting a new web platform to promote online education.

Mr. Zhao has also expressed interest in investing in artificial intelligence and biotechnology, and has corresponded with other executives. Late last year, he and Mr. Altman exchanged text messages, two people familiar with the matter said, and discussed the challenges of expanding a start-up worldwide.

Many powerful crypto executives have faced federal lawsuits and criminal charges since the multitrillion-dollar industry imploded in 2022. Some have gone to prison, while others have enjoyed the high life before being arrested. Mr. Zhao’s fate is likely to be kinder than most.

His frenetic activity since November contrasts with the consequences faced by Sam Bankman-Fried, the founder of the collapsed crypto exchange FTX. Once Mr. Zhao’s greatest rival, Mr. Bankman-Fried was largely ostracized after FTX imploded in 2022 and prosecutors charged him with stealing $8 billion in customer funds. A jury found him guilty of fraud last year, and he was sentenced in March to 25 years in prison.

Mr. Zhao, who pleaded guilty three weeks after Mr. Bankman-Fried was convicted at trial, still enjoys widespread support in the crypto industry. Dozens of current and former Binance employees have submitted letters to Judge Richard A. Jones, the federal judge overseeing Mr. Zhao’s case, asking him to impose a lenient sentence. And many crypto entrepreneurs, investors and dignitaries have continued supporting Mr. Zhao, court records show.

A short prison stint “is a small price to pay to be a billionaire for life,” said John Reed Stark, a former Securities and Exchange Commission official and a critic of the crypto industry. “The industry just does not care about the extraordinary crypto crime wave ushered in by people like CZ.”

Representatives for Mr. Zhao and OpenAI declined to comment.

For much of Binance’s existence, Mr. Zhao was dogged by accusations that he had broken the law to build a crypto empire. Binance was the world’s largest crypto exchange, processing as much as two-thirds of all transactions. And Mr. Zhao became a crypto celebrity, with nearly nine million followers on X. His posts helped set off a chain of events that led to FTX’s demise in 2022.

Last year, Binance faced its own reckoning. The company agreed to pay $4.3 billion to the U.S. government to settle charges that it allowed criminal activity to flourish on the exchange.

U.S. officials said Binance violated economic sanctions, allowing access to its platform to people in countries like Cuba, Syria and Iran. Mr. Zhao failed to set up proper anti-money-laundering controls, prosecutors said, and let customers sign up for accounts without providing the basic personal details that financial services firms usually require.

“Zhao violated U.S. law on an unprecedented scale,” prosecutors wrote in a court filing on Wednesday. “Zhao’s sentence should reflect the gravity of his crimes.”

Mr. Zhao started talking about his next act the moment the charge against him was announced. In a post on X the day of his plea hearing in November, for which he appeared in person in federal court in Seattle, he said he was interested in investing in areas like crypto, biotechnology and A.I.

“I may be open to being a coach/mentor to a small number of upcoming entrepreneurs,” he wrote. “If for nothing else, I can at least tell them what not to do.”

In a filing last week, prosecutors said Mr. Zhao had traveled throughout the United States, visiting New York, Los Angeles, Telluride and Moab. Mr. Zhao, who grew up partly in Canada, has spent some of his free time skiing and snowboarding, a person who knows him said.

Mr. Zhao met Mr. Altman in person about a year ago, a person with knowledge of the matter said. They were in contact again after a leadership battle at OpenAI in late November, two people familiar with the exchange said. The next month, over hot pot in Los Angeles, Mr. Zhao told Ronghui Gu, a computer science professor at Columbia University, that he had communicated with Mr. Altman.

“He talked to Sam, and they both believe that A.I. is going to help a lot in actualizing the development of technology and human knowledge,” Mr. Gu, who founded a start-up that Binance helped fund, said in an interview.

At the same meal, Mr. Zhao mentioned that he was “looking for opportunities” to invest in the large data centers that power A.I. applications, Mr. Gu said.

(The New York Times has sued OpenAI and its partner, Microsoft, claiming copyright infringement of news content related to A.I. systems.)

In a letter filed in court last week, Mr. Zhao said he had also spoken with “a number of biotech start-ups” in recent months and planned to make disease prevention a focus in the next chapter of his life.

“I’d like to help fund small research labs with the aim of curing diseases once and for all, as well as providing medical access to billions in the world using blockchain technologies,” he wrote.

In March, Mr. Zhao announced on X that he was starting a project called Giggle Academy, a free online learning platform for children. A seven-page “concept paper” posted on Giggle Academy’s website said the platform would involve A.I. and automation, as well as nonfungible tokens, the unique digital collectibles known as NFTs.

Mr. Zhao wrote on X that Giggle Academy would have “no revenue” and that he was recruiting a small team to work directly with him.

On his travels, Mr. Zhao has also caught up with influential acquaintances. A couple of months ago, he had dinner at the Montana home of Max Baucus, a former U.S. senator and ambassador to China. In a letter filed in court last week, Mr. Baucus, who worked for Binance as an adviser, said he and Mr. Zhao had discussed the criminal case.

“He didn’t make any excuses except to note he didn’t hurt anyone,” wrote Mr. Baucus, a Democrat. “He didn’t use others funds for his own account distinguishing him from Sam Bankman-Fried, who did just that.”

At the dinner with Mr. Gu in December, Mr. Zhao was joined by his son, a freshman at Pepperdine University. The dinner was mostly casual, Mr. Gu wrote in a letter to the court last week. He and Mr. Zhao discussed their shared interest in crypto, as well as “insights on being a good C.E.O.”

Then Mr. Zhao’s son asked his father whether he was really guilty. “The sudden silence that followed was palpable,” Mr. Gu wrote. “He acknowledged his mistakes and his guilt, emphasizing that making mistakes is not something to be ashamed of.”

Mr. Zhao soon lightened the mood, the letter said, cracking a joke about Mr. Gu’s “continued willingness to dine with them.”

Kitty Bennett contributed research.