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Search: id:A030285
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| A030285 |
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Palindromes whose digits do not appear in previous term. |
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+0
1
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 222, 303, 414, 505, 616, 707, 818, 909, 1111, 2002, 3113, 4004, 5115, 6006, 7117, 8008, 9119, 20002, 31113, 40004, 51115, 60006, 71117, 80008, 91119, 200002, 311113, 400004
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A062687 A109882 A109872 this_sequence A048321 A071267 A110784
Adjacent sequences: A030282 A030283 A030284 this_sequence A030286 A030287 A030288
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com)
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2003
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