A030285 Palindromes whose digits do not appear in previous term.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..48.

Mathematica

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}]

Crossrefs

Sequence in context: A062687 A109882 A109872 * A283870 A175688 A048321

Adjacent sequences: A030282 A030283 A030284 * A030286 A030287 A030288

Keyword

nonn,base

Author

Patrick De Geest

Extensions

Edited by Robert G. Wilson v, Jun 27 2003

Status

approved