Agency Conferences and Conventions Operating Under Necessary Transparency Act of 2013 or the ACCOUNT Act - Requires the head of a federal agency to: (1) approve in writing any conference costing more than $25,000, (2) approve such a conference only upon determining that it is necessary to the core mission of the agency, and (3) publish a summary on the agency website of the conference that includes the purpose and total cost of the conference and the cost per employee that attended the conference. Excludes conferences held entirely at a government facility.