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Palindromes whose digits do not appear in previous term.
0

%I #8 Aug 24 2012 10:47:39

%S 0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,222,303,414,505,

%T 616,707,818,909,1111,2002,3113,4004,5115,6006,7117,8008,9119,20002,

%U 31113,40004,51115,60006,71117,80008,91119,200002,311113,400004

%N Palindromes whose digits do not appear in previous term.

%C Although the sequence is infinite, in a sense it cycles. The outside of the next palindrome beginning with 20 continues 31, 40, 51, 60, 71, 80, 91 and back to 20. The inside oscillates between increasing number of zeros and ones.

%t NextPalindrome[n_] := Block[{l = Floor[Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]]]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[ Reverse[ IntegerDigits[idfhn]], Mod[l, 2]]]]]]]]; a[0] = 0; a[n_] := a[n] = Block[{k = a[n - 1], d = IntegerDigits[a[n - 1]]}, While[ Intersection[d, IntegerDigits[k]] != {}, k = NextPalindrome[k]]; k]; Table[ a[n], {n, 0, 50}]

%K nonn,base

%O 1,3

%A _Patrick De Geest_

%E Edited by _Robert G. Wilson v_, Jun 27 2003