A140268 a(n) = negative integer -n presented in balanced ternary system.

2, 21, 20, 22, 211, 210, 212, 201, 200, 202, 221, 220, 222, 2111, 2110, 2112, 2101, 2100, 2102, 2121, 2120, 2122, 2011, 2010, 2012, 2001, 2000, 2002, 2021, 2020, 2022, 2211, 2210, 2212, 2201, 2200, 2202, 2221, 2220, 2222, 21111, 21110, 21112

Offset: 1

Author

Antti Karttunen, May 19 2008, prompted by Eric Angelini's posting on SeqFan mailing list on Sep 15 2005

Keywords

• nonn
• base

Comments

Sequence A117968 in ternary. (See there for more references.)

Examples

			For example a(2) = 21, as -2 = -1*3 + 1*1.
Similarly, a(19) = 2102, as -19 = -1*27 + 1*9 + 0*3 + -1*1.
		

Crossrefs

a(n) = A007089(A117968(n)). Cf. A140267.

Programs

Python

from sympy.ntheory.factor_ import digits
def a117968(n):
    if n==1: return 2
    if n%3==0: return 3*a117968(n/3)
    elif n%3==1: return 3*a117968((n - 1)/3) + 2
    else: return 3*a117968((n + 1)/3) + 1
def a(n): return int("".join(map(str, digits(a117968(n), 3)[1:]))) # Indranil Ghosh, Jun 06 2017