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A257868 Negative integers n such that in balanced ternary representation the number of occurrences of each trit doubles when n is squared.

%I A257868 #20 May 08 2021 11:23:36
%S A257868 -314,-898,-942,-2694,-2824,-2826,-2962,-3014,-3070,-3074,-8066,-8082,
%T A257868 -8090,-8096,-8132,-8170,-8224,-8336,-8426,-8434,-8450,-8472,-8478,
%U A257868 -8480,-8618,-8656,-8870,-8886,-8918,-9008,-9042,-9210,-9222,-9224,-24198,-24226,-24246
%N A257868 Negative integers n such that in balanced ternary representation the number of occurrences of each trit doubles when n is squared.
%H A257868 Alois P. Heinz, <a href="/A257868/b257868.txt">Table of n, a(n) for n = 1..10000</a>
%H A257868 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%e A257868 -898 is in the sequence because -898 = LL10L1L_bal3 and (-898)^2 = 806404 = 1LLLL00L1LLL11_bal3, where L represents (-1).
%p A257868 p:= proc(n) local d, m, r; m:=abs(n); r:=0;
%p A257868       while m>0 do
%p A257868         d:= irem(m, 3, 'm');
%p A257868         if d=2 then m:=m+1 fi;
%p A257868         r:=r+x^`if`(n>0, d, irem(3-d, 3))
%p A257868       od; r
%p A257868     end:
%p A257868 a:= proc(n) option remember; local k;
%p A257868       for k from -1+`if`(n=1, 0, a(n-1)) by -1
%p A257868       while p(k)*2<>p(k^2) do od; k
%p A257868     end:
%p A257868 seq(a(n), n=1..50);
%o A257868 (Python)
%o A257868 def a(n):
%o A257868     s=[]
%o A257868     l=[]
%o A257868     x=0
%o A257868     while n>0:
%o A257868         x=n%3
%o A257868         n//=3
%o A257868         if x==2:
%o A257868             x=-1
%o A257868             n+=1
%o A257868         s.append(x)
%o A257868         l.append(-x)
%o A257868     return [s, l]
%o A257868 print([-n for n in range(1, 25001) if a(n**2)[0].count(-1)==2*a(n)[1].count(-1) and a(n**2)[0].count(1)==2*a(n)[1].count(1) and a(n**2)[0].count(0)==2*a(n)[1].count(0)]) # _Indranil Ghosh_, Jun 07 2017
%Y A257868 Cf. A117967, A140267, A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A114258, A257867, A257869.
%K A257868 sign,base
%O A257868 1,1
%A A257868 _Alois P. Heinz_, May 11 2015