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A257869 Nonnegative integers with an equal number of occurrences of all trits in balanced ternary representation.

%I A257869 #19 May 06 2021 11:04:31
%S A257869 6,8,136,138,144,154,156,160,164,168,170,180,186,188,208,210,214,218,
%T A257869 222,224,232,236,248,258,260,266,288,294,296,312,314,320,3406,3412,
%U A257869 3414,3430,3432,3438,3484,3486,3492,3510,3568,3574,3576,3592,3594,3600,3622
%N A257869 Nonnegative integers with an equal number of occurrences of all trits in balanced ternary representation.
%H A257869 Alois P. Heinz, <a href="/A257869/b257869.txt">Table of n, a(n) for n = 1..10000</a>
%H A257869 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%e A257869 6 = 1L0_bal3, 8 = 10L_bal3, 136 = 1LL001_bal3, 138 = 1LL010_bal3, 144 = 1LL100_bal3, where L represents (-1).
%p A257869 p:= proc(n) local d, m, r; m:=n; r:=0;
%p A257869       while m>0 do
%p A257869         d:= irem(m, 3, 'm');
%p A257869         if d=2 then m:=m+1 fi;
%p A257869         r:= r+x^d
%p A257869       od;
%p A257869       simplify(r/(1+x+x^2))::integer
%p A257869     end:
%p A257869 a:= proc(n) option remember; local k;
%p A257869       for k from 1+`if`(n=1, 0, a(n-1)) by 1
%p A257869       while not p(k) do od; k
%p A257869     end:
%p A257869 seq(a(n), n=1..70);
%o A257869 (Python)
%o A257869 def a(n):
%o A257869     s=[]
%o A257869     x=0
%o A257869     while n>0:
%o A257869         x=n%3
%o A257869         n//=3
%o A257869         if x==2:
%o A257869             x=-1
%o A257869             n+=1
%o A257869         s.append(x)
%o A257869     return s
%o A257869 print([n for n in range(1, 5001) if a(n).count(1)==a(n).count(-1) and a(n).count(-1)==a(n).count(0)]) # _Indranil Ghosh_, Jun 07 2017
%Y A257869 Cf. A117967, A140267, A257867, A257868, A258410.
%Y A257869 Subsequence of A174658.
%K A257869 nonn,base
%O A257869 1,1
%A A257869 _Alois P. Heinz_, May 11 2015