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A233572 In balanced ternary notation, if prepending same numbers of zeros, reverse digits of a(n) equals to -a(n).

%I A233572 #8 Jun 02 2025 08:53:12
%S A233572 0,2,6,8,18,20,24,26,32,54,56,60,72,78,80,96,104,146,162,164,168,180,
%T A233572 182,216,224,234,240,242,260,288,302,312,320,338,416,438,486,488,492,
%U A233572 504,540,546,560,648,656,672,702,720,726,728,780,800,864,896,906,936
%N A233572 In balanced ternary notation, if prepending same numbers of zeros, reverse digits of a(n) equals to -a(n).
%C A233572 A233571 is a subset of this sequence.
%H A233572 Lei Zhou, <a href="/A233572/b233572.txt">Table of n, a(n) for n = 1..10000</a>
%e A233572 In balanced ternary notation, 18 = (1T00)_bt, where we use T to represent -1.  Patching two zeros before it, (1T00)_bt=(001T00)_bt.  The reverse digits of (001T00)_bt is (00T100)_bt = -18.  So 18 is in this sequence.
%t A233572 BTDigits[m_Integer, g_] :=
%t A233572 Module[{n = m, d, sign, t = g},
%t A233572   If[n != 0, If[n > 0, sign = 1, sign = -1; n = -n];
%t A233572    d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++];
%t A233572    While[Length[t] < d, PrependTo[t, 0]]; t[[Length[t] + 1 - d]] = sign;
%t A233572    t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];
%t A233572 BTrteQ[n_Integer] :=
%t A233572 Module[{t, trim = n/3^IntegerExponent[n, 3]},
%t A233572   t = BTDigits[trim, {0}]; DeleteDuplicates[t + Reverse[t]] == {0}];
%t A233572 sb = Select[Range[0, 950], BTrteQ[#] &]
%Y A233572 Cf. A002113, A061917, A006995, A057890, A134027, A233010, A233571
%K A233572 nonn,base
%O A233572 1,2
%A A233572 _Lei Zhou_, Dec 13 2013