Enumerate all number that are palindromic in at least two of base 2, 8, 10, 16 or 64
Mathematica
f[number,minPalindromeLength,minCount]works as follows If number is a palindrome with minPalindromeLength in at least minCount bases, f returns the information about that number.
g[max,minPalindromeLength,minCount] makes an table of &quot;palindrome numbers&quot; from 1 through max.
f[number_,minPalindromeLength_:2,minCount_:2]:=Module[{print,palindromeQ,count, 
convert64=Thread[Range[0,63]-&gt;Characters[&quot;0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ@_&quot;]],
digits=IntegerDigits[number,#]&amp;/@(bases={64,16,10,8,2})},
palindromeQ[dig_]:=(dig==Reverse[dig]);
count = Total@Boole[palindromeQ/@ Cases[digits,x_/;Length[x]&gt;minPalindromeLength-1]];
If[count&gt;minCount-1,Join[{count,Subscript[StringJoin[IntegerDigits[number,64]/.convert64],64]},BaseForm[number,#]&amp;/@Rest[bases]],Sequence[]]];

g[max_,minPalindromeLength_:2,minCount_:2]:=
(Print[&quot;\nPalindromes: minPalindromeLength = &quot;,minPalindromeLength &quot;\tand minCount &quot;, minCount ]; 
DeleteCases[Table[f[z,minPalindromeLength,minCount],{z,9,max}],Null]//Grid);

g[5000,2,3]
g[5000,3,3]
g[5000,4,2]