Numbers that are palindromes in N bases
Mathematica, 80 71 bytes

Thanks to JungHwan Min for saving 9 bytes!

Do[#!=Length[i~IntegerReverse~Range[2,i-2]~Cases~i]||Echo@i,{i,3,∞}]&amp;


(∞ is the three-byte character U+221E.)
Pure function taking a nonnegative integer as input. i~IntegerReverse~Range[2,i-2] creates a list of the reversals of the number i in all the bases from 2 to i-2; then Length[...~Cases~i] counts how many of these reversals are equal to i again. #!=...||Echo@i halts silently if that count is not equal to the input, and echoes i if it is equal to the input. That procedure is embedded in a straightforward infinite loop.