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A214425
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Numbers n palindromic in exactly three bases b, 2 <= b <= 10.
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8
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9, 10, 21, 40, 55, 63, 65, 80, 85, 100, 130, 154, 164, 178, 191, 195, 203, 235, 242, 255, 257, 273, 282, 292, 300, 325, 328, 341, 400, 455, 585, 656, 819, 910, 2709, 4095, 4097, 4161, 6643, 8200, 12291, 12483, 14762, 20485, 20805, 21525, 21845, 32152, 53235
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OFFSET
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1,1
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COMMENTS
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In the first 1234 terms, only 28 of the possible 84 triples of bases occur. Does every triple occur eventually? - T. D. Noe, Aug 17 2012
See A238893 for the three bases. By far, the most common bases are (2,4,8). - T. D. Noe, Mar 07 2014 (exception are in A260184. - Giovanni Resta and Robert G. Wilson v, Jul 17 2015).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1234
Rick Regan, Finding numbers that are palindromic in multiple bases
Index entries for sequences related to palindromes
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FORMULA
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A050812(n) = 3.
The intersection of A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955 & A002113 which yields just three members. - Giovanni Resta and Robert G. Wilson v, Jul 17 2015
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EXAMPLE
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10 is palindromic in bases 3, 4, and 9.
273 is in the sequence because 100010001_2 = 101010_3 = 10101_4 = 2043_5 = 1133_6 = 540_7 = 421_8 = 333_9 = 273_10 and three of the bases, namely 2, 4 & 9, yield palindromes. - Giovanni Resta and Robert G. Wilson v, Jul 17 2015
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MATHEMATICA
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n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 3, AppendTo[t, n]]]; t
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CROSSREFS
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Cf. A050813, A214423, A214424, A214426 (palindromic in 0-2 and 4 bases).
Sequence in context: A085949 A102238 A104646 * A260184 A109463 A326523
Adjacent sequences: A214422 A214423 A214424 * A214426 A214427 A214428
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KEYWORD
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nonn,base
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AUTHOR
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T. D. Noe, Jul 18 2012
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STATUS
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approved
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