%I #19 Sep 08 2021 13:08:41

%S 0,1,2,4,28,80,160,203,560,644,910,34216,34972,74647,87763,122420,

%T 221068,225064,6731644,6877120,6927700,7723642,8128762,8271430,

%U 77894071,78526951,539212009,28476193256,200267707484,200316968444,201509576804,201669082004,231852949304,232018753064,232039258376,333349186006,2947903946317,5816975658914,5817003372578,11610051837124,27950430282103,81041908142188

%N Palindromic numbers in bases 3 and 6 written in base 10.

%C Agrees with the number of minimal dominating sets of the halved cube graph Q_n/2 for at least n=1 to 5. - _Eric W. Weisstein_, Sep 06 2021

%H Giovanni Resta, <a href="/A259375/b259375.txt">Table of n, a(n) for n = 1..64</a>

%F Intersection of A014190 and A029953.

%e 28 is in the sequence because 28_10 = 44_6 = 1001_3.

%t (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 6]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst

%t b1=3; b2=6; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* _Vincenzo Librandi_, Jul 15 2015 *)

%Y Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

%K nonn,base

%O 1,3

%A Eric A. Schmidt and _Robert G. Wilson v_, Jul 14 2015