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

-314, -898, -942, -2694, -2824, -2826, -2962, -3014, -3070, -3074, -8066, -8082, -8090, -8096, -8132, -8170, -8224, -8336, -8426, -8434, -8450, -8472, -8478, -8480, -8618, -8656, -8870, -8886, -8918, -9008, -9042, -9210, -9222, -9224, -24198, -24226, -24246

Offset: 1

Author

Alois P. Heinz, May 11 2015

Keywords

• sign
• base

Examples

			-898 is in the sequence because -898 = LL10L1L_bal3 and (-898)^2 = 806404 = 1LLLL00L1LLL11_bal3, where L represents (-1).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Wikipedia, Balanced ternary

Crossrefs

Cf. A117967, A140267, A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A114258, A257867, A257869.

Programs

Maple

p:= proc(n) local d, m, r; m:=abs(n); r:=0;
      while m>0 do
        d:= irem(m, 3, 'm');
        if d=2 then m:=m+1 fi;
        r:=r+x^`if`(n>0, d, irem(3-d, 3))
      od; r
    end:
a:= proc(n) option remember; local k;
      for k from -1+`if`(n=1, 0, a(n-1)) by -1
      while p(k)*2<>p(k^2) do od; k
    end:
seq(a(n), n=1..50);

Python

def a(n):
    s=[]
    l=[]
    x=0
    while n>0:
        x=n%3
        n//=3
        if x==2:
            x=-1
            n+=1
        s.append(x)
        l.append(-x)
    return [s, l]
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