A320636 - OEIS

%I #15 Dec 11 2021 10:40:03

%S 12,11,10,22,21,20,1202,1201,1200,1212,1211,1210,1222,1221,1220,1102,

%T 1101,1100,1112,1111,1110,1122,1121,1120,1002,1001,1000,1012,1011,

%U 1010,1022,1021,1020,2202,2201,2200,2212,2211,2210,2222,2221,2220,2102,2101,2100,2112

%N Negative numbers in base -3.

%C Extend A073785 to negative-indexed terms, then a(n) = A073785(-n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Negadecimal.html">Negadecimal</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Negabinary.html">Negabinary</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Negative_base">Negative base</a>

%e -7 in base -3 is represented as 1202 (1*(-3)^3 + 2*(-3)^2 + 2 = -7), so a(7) = 1202;

%e -16 in base -3 is represented as 1102 (1*(-3)^3 + 1*(-3)^2 + 2 = -16), so a(16) = 1102;

%e -40 in base -3 is represented as 2222 (2*(-3)^3 + 2*(-3)^2 + 2*(-3) + 2 = -99), so a(40) = 2222.

%o (PARI) A073785 = base(n, b=-3) = if(n, base(n\b, b)*10 + n%b, 0)

%o a(n) = A073785(-n)

%o (Python)

%o def A073785(n): # after _Reinhard Zumkeller_

%o     if n == 0: return 0

%o     (q, r) = divmod(n, -3)

%o     (nn, m) = (q, r) if r >= 0 else (q+1, r+3)

%o     return A073785(nn)*10 + m

%o def a(n): return A073785(-n)

%o print([a(n) for n in range(1, 47)]) # _Michael S. Branicky_, Dec 11 2021

%Y Nonnegative numbers in negative bases: A039723 (b=-10), A039724 (b=-2), A073785 (b=-3), A007608 (b=-4), A073786 (b=-5), A073787 (b=-6), A073788 (b=-7), A073789 (b=-8), A073790 (b=-9).

%Y Negative numbers in negative bases: A305238 (b=-10), A212529 (b=-2), this sequence (b=-3), A212526 (b=-4).

%K nonn,base

%O 1,1

%A _Jianing Song_, Oct 18 2018