WASHINGTON — An inflation gauge favored by the Federal Reserve increased in January, the latest sign that the slowdown in U.S. consumer price increases is occurring unevenly from month to month. The government reported Thursday that prices rose 0.3% from December to January, up from 0.1% in the previous month. But in a more encouraging sign, prices were up just 2.4% from a year earlier, down from a 2.6% annual pace in December and the smallest such increase in nearly three years. The year-over-year cooldown in inflation is sure to be …