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A355640 a(0) = 0, and for any n > 0, a(n) is the least positive multiple of n whose balanced ternary expansion contains as many negative trits as positive trits.

%I A355640 #6 Jul 13 2022 14:43:36
%S A355640 0,2,2,6,8,20,6,56,8,18,20,154,24,26,56,60,16,136,18,266,20,168,154,
%T A355640 46,24,400,26,54,56,232,60,62,32,462,136,70,72,74,266,78,80,164,168,
%U A355640 86,440,180,46,188,48,98,400,408,52,424,54,440,56,798,232,236,60
%N A355640 a(0) = 0, and for any n > 0, a(n) is the least positive multiple of n whose balanced ternary expansion contains as many negative trits as positive trits.
%C A355640 A174658 corresponds to fixed points.
%F A355640 a(n) = n * A355639(n).
%e A355640 For n = 5:
%e A355640 - the first multiple of 5 (alongside their balanced ternary expansions) are:
%e A355640       k  k*5  bter(k*5)  #1  #T
%e A355640       -  ---  ---------  --  --
%e A355640       1    5        1TT   1   2
%e A355640       2   10        101   2   0
%e A355640       3   15       1TT0   1   2
%e A355640       4   20       1T1T   2   2
%e A355640 - negative and positive trits are first balanced for k = 4,
%e A355640 - so a(5) = 4*5 = 20.
%o A355640 (PARI) a(n) = { for (k=1, oo, my (m=k*n, s=0, d); while (m, m=(m-d=[0, 1, -1][1+m%3])/3; s+=d); if (s==0, return (k*n))) }
%Y A355640 See A143146 for a similar sequence.
%Y A355640 Cf. A065363, A174658 (fixed points), A355639.
%K A355640 nonn,base
%O A355640 0,2
%A A355640 _Rémy Sigrist_, Jul 11 2022