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A214425 Numbers n palindromic in exactly three bases b, 2 <= b <= 10. 8

%I #23 Aug 07 2015 19:29:19

%S 9,10,21,40,55,63,65,80,85,100,130,154,164,178,191,195,203,235,242,

%T 255,257,273,282,292,300,325,328,341,400,455,585,656,819,910,2709,

%U 4095,4097,4161,6643,8200,12291,12483,14762,20485,20805,21525,21845,32152,53235

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

%C 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

%C 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).

%H T. D. Noe, <a href="/A214425/b214425.txt">Table of n, a(n) for n = 1..1234</a>

%H Rick Regan, <a href="http://www.exploringbinary.com/finding-numbers-that-are-palindromic-in-multiple-bases/">Finding numbers that are palindromic in multiple bases</a>

%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>

%F A050812(n) = 3.

%F 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

%e 10 is palindromic in bases 3, 4, and 9.

%e 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

%t 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

%Y Cf. A050813, A214423, A214424, A214426 (palindromic in 0-2 and 4 bases).

%K nonn,base

%O 1,1

%A _T. D. Noe_, Jul 18 2012

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