A257868 -id:A257868 - cp's OEIS frontend

A257869 Nonnegative integers with an equal number of occurrences of all trits in balanced ternary representation.

6, 8, 136, 138, 144, 154, 156, 160, 164, 168, 170, 180, 186, 188, 208, 210, 214, 218, 222, 224, 232, 236, 248, 258, 260, 266, 288, 294, 296, 312, 314, 320, 3406, 3412, 3414, 3430, 3432, 3438, 3484, 3486, 3492, 3510, 3568, 3574, 3576, 3592, 3594, 3600, 3622

Offset: 1

Alois P. Heinz, May 11 2015

			6 = 1L0_bal3, 8 = 10L_bal3, 136 = 1LL001_bal3, 138 = 1LL010_bal3, 144 = 1LL100_bal3, where L represents (-1).

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

Cf. A117967, A140267, A257867, A257868, A258410.

Subsequence of A174658.

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;
      simplify(r/(1+x+x^2))::integer
    end:
a:= proc(n) option remember; local k;
      for k from 1+`if`(n=1, 0, a(n-1)) by 1
      while not p(k) do od; k
    end:
seq(a(n), n=1..70);

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, 5001) if a(n).count(1)==a(n).count(-1) and a(n).count(-1)==a(n).count(0)]) # Indranil Ghosh, Jun 07 2017

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

Original entry on oeis.org

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

Alois P. Heinz, May 11 2015

			942 is in the sequence because 942 = 110L0L0_bal3 and 942^2 = 887364 = 1LL0001L1L0100_bal3, where L represents (-1).

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

Cf. A117967, A140267, A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A114258, A257868, A257869, A258411.

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);

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

cp's OEIS Frontend

A257869 Nonnegative integers with an equal number of occurrences of all trits in balanced ternary representation.

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