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A257867 Nonnegative integers n such that in balanced ternary representation the number of occurrences of each trit doubles when n is squared.

%I A257867 #22 May 07 2021 09:10:22
%S A257867 314,942,2824,2826,2854,3074,3130,3212,8066,8090,8096,8170,8224,8324,
%T A257867 8426,8450,8472,8478,8480,8512,8534,8562,8578,8588,8656,9222,9224,
%U A257867 9390,9404,9636,9638,24198,24206,24270,24288,24510,24670,24672,24674,24676,24802,24972
%N A257867 Nonnegative integers n such that in balanced ternary representation the number of occurrences of each trit doubles when n is squared.
%H A257867 Alois P. Heinz, <a href="/A257867/b257867.txt">Table of n, a(n) for n = 1..10000</a>
%H A257867 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%e A257867 942 is in the sequence because 942 = 110L0L0_bal3 and 942^2 = 887364 = 1LL0001L1L0100_bal3, where L represents (-1).
%p A257867 p:= proc(n) local d, m, r; m:=n; r:=0;
%p A257867       while m>0 do
%p A257867         d:= irem(m,3,'m');
%p A257867         if d=2 then m:=m+1 fi;
%p A257867         r:=r+x^d
%p A257867       od; r
%p A257867     end:
%p A257867 a:= proc(n) option remember; local k;
%p A257867       for k from 1+`if`(n=1, 0, a(n-1))
%p A257867       while p(k)*2<>p(k^2) do od; k
%p A257867     end:
%p A257867 seq(a(n), n=1..50);
%o A257867 (Python)
%o A257867 def a(n):
%o A257867     s=[]
%o A257867     x=0
%o A257867     while n>0:
%o A257867         x=n%3
%o A257867         n//=3
%o A257867         if x==2:
%o A257867             x=-1
%o A257867             n+=1
%o A257867         s.append(x)
%o A257867     return s
%o A257867 print([n for n in range(1, 25001) if a(n**2).count(-1)==2*a(n).count(-1) and a(n**2).count(1)==2*a(n).count(1) and a(n**2).count(0)==2*a(n).count(0)]) # _Indranil Ghosh_, Jun 07 2017
%Y A257867 Cf. A117967, A140267, A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A114258, A257868, A257869, A258411.
%K A257867 nonn,base
%O A257867 1,1
%A A257867 _Alois P. Heinz_, May 11 2015