Palindromic num3ers: Searching for 3-digit numbers such as

Here we search for 3-digit numbers that are palindromic in other bases, base 2, 3, 4, 5, 6, 7, 8 and 9.

The tool I'm using is :

http://www.cleavebooks.co.uk/scol/calnumba.htm

For example,

Base 10 .................. Palindromic in base(s)
100 .......................... 1 0201 (base 3), 202 (base 7), 121 (base 9)

101 .......................... NO

102 .......................... NO

103 .......................... NO

104 .......................... 404 (base 5), 252 (base 6)

105 .......................... 1221 (base 4), 151 (base 8)

106 .......................... NO

107 .......................... 110 1011 (base 2), 212 (base 7)

108 .......................... NO

109 .......................... 414 (base 5), 131 (base 9)

110 .......................... NO

111 ........................... 303 (base 6)

112 ........................... 11011 (base 3)

113 ........................... NO

114 ........................... 424 (base 5), 222 (base 7)

115 ........................... NO

116 ........................... NO

117 ........................... 313 (base 6)

118 ........................... 141 (base 9)

119 ........................... 1110111 (base 2), 434 (base 5)

120 ........................... NO

121 ............................ 11111 (base 3), 232 (base 7), 171 (base 8)

122

123

124

Could you show how to find such numbers without going thru all 3-digit numbers?