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%I #16 Jul 28 2016 11:25:22
%S 5,7,9,10,13,15,16,17,20,21,23,25,26,27,28,29,31,33,34,36,37,38,40,41,
%T 42,43,45,46,49,50,51,52,55,56,57,59,61,62,63,64,65,67,68,71,72,73,74,
%U 78,80,81,82,83,85,86,88,89,91,92,93,97,98,99,100,101,104,105,107,109
%N Numbers that are nontrivial (3 digits or more) palindromes when expressed in some base 2 or greater.
%C All integers are trivially palindromes in base 1. All integers n>2 are trivially 2-digit palindromes because they can be represented as "11" in base n-1.
%e 5 is present because the palindrome (101 base 2) = 5; 803 is present because (30203 base 4) = 803.
%t palindromeQ[n_, b_] := (id = IntegerDigits[n, b]) === Reverse[id] && Length[id] >= 3; palindromeQ[n_] := Or @@ (palindromeQ[n, #] & ) /@ Range[2, n-2]; Select[ Range[110], palindromeQ] (* _Jean-François Alcover_, Dec 16 2011 *)
%o (Haskell) isPalindrome s = (s == reverse s) digits 0 _ = [] digits n b = n `rem` b : digits (n `quot` b) b check n = any isPalindrome $ takeWhile (\x -> length x > 2) $ map (digits n) [2..] main = mapM print $ filter check [1..]
%o (PARI) isok(n) = for (b=2, n-1, if ((d=digits(n,b)) && (#d >= 3) && (Vecrev(d) == d), return (1));); \\ _Michel Marcus_, Jul 28 2016
%Y Cf. A060873-A060879, A060947-A060949, A123586.
%K easy,base,nonn
%O 1,1
%A Jason Orendorff (jason.orendorff(AT)gmail.com), Feb 05 2006
%E Cross-references from _Charles R Greathouse IV_, Aug 04 2010
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