

A214425


Numbers n palindromic in exactly three bases b, 2 <= b <= 10.


8



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

1,1


COMMENTS

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).


LINKS

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


FORMULA

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


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A050813, A214423, A214424, A214426 (palindromic in 02 and 4 bases).
Sequence in context: A085949 A102238 A104646 * A260184 A109463 A061410
Adjacent sequences: A214422 A214423 A214424 * A214426 A214427 A214428


KEYWORD

nonn,base


AUTHOR

T. D. Noe, Jul 18 2012


STATUS

approved



