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.