A327252 - OEIS

%I #41 Sep 20 2019 10:49:41

%S 0,1,-1,1,4,-2,-1,2,-4,1,10,-8,4,13,-5,-2,7,-11,-1,8,-10,2,11,-7,-4,5,

%T -13,1,28,-26,10,37,-17,-8,19,-35,4,31,-23,13,40,-14,-5,22,-32,-2,25,

%U -29,7,34,-20,-11,16,-38,-1,26,-28,8,35,-19,-10,17,-37,2,29,-25,11

%N Balanced reversed ternary: Write n as ternary, reverse the order of the digits, then replace all 2's with (-1)'s.

%H Rémy Sigrist, <a href="/A327252/b327252.txt">Table of n, a(n) for n = 0..19683</a>

%e 5 in base 3 is 12; reversing the ternary gives 21; replacing the 2 with (-1) gives (-1),1 which is -2 in decimal.

%p a:= proc(n) local m, r; m, r:= n, 0;

%p       while m>0 do m, r:= iquo(m, 3), 3*r+mods(m, 3) od; r

%p     end:

%p seq(a(n), n=0..3^4-1);  # _Alois P. Heinz_, Sep 17 2019

%t a[n_] := FromDigits[Reverse[IntegerDigits[n, 3]] /. {2 -> -1}, 3]; Array[a, 67, 0] (* _Giovanni Resta_, Sep 17 2019 *)

%o (Python)

%o def a(n):

%o     ternary = []

%o     i = math.floor(math.log(n,3))

%o     while i >= 0:

%o         for j in range (2, -1, -1):

%o             if j*(3**i) <= n:

%o                 if (j==2): ternary.append(-1)

%o                 else: ternary.append(j)

%o                 n -= j*(3**i)

%o                 break

%o         i -=1

%o     for k in range (0, len(ternary)):

%o         n += ternary[k]*(3**k)

%o     return n

%o (PARI) a(n) = fromdigits(apply(d -> if (d==2, -1, d), Vecrev(digits(n,3))), 3) \\ _Rémy Sigrist_, Sep 15 2019

%Y Cf. A134028 (reversed balanced ternary, i.e. balancing the ternary, then reversing the ternary and transforming back into decimal), A117966 (balanced ternary enumeration).

%K sign,look,base

%O 0,5

%A _Elisabeth Zemack_, Sep 15 2019