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

314, 942, 2824, 2826, 2854, 3074, 3130, 3212, 8066, 8090, 8096, 8170, 8224, 8324, 8426, 8450, 8472, 8478, 8480, 8512, 8534, 8562, 8578, 8588, 8656, 9222, 9224, 9390, 9404, 9636, 9638, 24198, 24206, 24270, 24288, 24510, 24670, 24672, 24674, 24676, 24802, 24972

Offset: 1

Author

Alois P. Heinz, May 11 2015

Keywords

• nonn
• base

Examples

			942 is in the sequence because 942 = 110L0L0_bal3 and 942^2 = 887364 = 1LL0001L1L0100_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, A257868, A257869, A258411.

Programs

Maple

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

Python

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