When nuclear-powered warships first entered discussion

When did serious discussion of nuclear-powered warships begin?

Very early in nuclear-power thinking, although this answer does not give a firm date for the first serious proposal.

Nuclear propulsion entered discussion as soon as nuclear power became conceivable. Large warships were natural candidates because their endurance and power demands made the possible economic advantage attractive. Early battleship proposals are recalled, but this clipped answer does not establish a reliable year. That early chronology matters because the later reactor counterfactual explores what practical early systems might do to capital-ship design.