No.
1001,1111,1221,1331,1441,1551,1661,1771,1881,1991,2002,2112,2222,2332,2442,2552,2662,2772,2882,2992,3003,3113,3223,3333,3443,3553,3663,3773,3883,3993,4004,4114,4224,4334,4444,4554,4664,4774,4884,4994: 40 numbers in all.
40 palindromes.
40. Excluding numbers starting with 0.
There are not just 13 non-palindromic numbers. Most numbers are non-palindromic.
There are 90 palindromic numbers between 100 and 1000
Whole number palindromes between 10 and 40 are: 11, 22, 33 There are, in theory, an infinite number of palindromic decimal numbers in between - but just three palindromic integers.
31 and 37
No.
Nobody went out to create them: some numbers simply happen to be palindromic and others don't.
infinite
777717711771817718817...
there are 10 palindromic numbers between 9000 and 10000 9009,9119,9229,9339,9449,9559,9669,9779,9889,9999!!!