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