The heads of the Pentagon and the nation’s intelligence community have recommended to President Obama that the director of the National Security Agency, Adm. Michael S. Rogers, be removed. The recommendation, delivered to the White House last month, was made by Defense Secretary Ashton B. Carter and Director of National Intelligence James R. Clapper Jr., according to several U.S. officials familiar with the matter. The news comes as Rogers is being considered by President-elect Donald Trump to be his nominee for director of national intelligence to replace Clapper as the official who oversees all 17 U.S. intelligence agencies. In a move apparently unprecedented for a military officer, Rogers, without notifying superiors, traveled to New York to meet with Trump on Thursday at Trump Tower. That caused consternation at senior levels of the administration.