A117968 Negative part of inverse of A117966; write -n in balanced ternary and then replace (-1)'s with 2's.

2, 7, 6, 8, 22, 21, 23, 19, 18, 20, 25, 24, 26, 67, 66, 68, 64, 63, 65, 70, 69, 71, 58, 57, 59, 55, 54, 56, 61, 60, 62, 76, 75, 77, 73, 72, 74, 79, 78, 80, 202, 201, 203, 199, 198, 200, 205, 204, 206, 193, 192, 194, 190, 189, 191, 196, 195, 197, 211, 210, 212, 208, 207

Offset: 1

Author

Franklin T. Adams-Watters, Apr 05 2006

Keywords

• base
• nonn

Examples

			-7 in balanced ternary is (-1)1(-1), changing to 212 ternary is 23, so a(7)=23.
		

References

• D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, pp. 173-175

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..6561
• Ken Levasseur, The Balanced Ternary Number System

Crossrefs

Cf. A117966. a(n) = A004488(A117967(n)). Bisection of A140263. A140268 gives the same sequence in ternary.

Programs

Python

def a(n):
    if n==1: return 2
    if n%3==0: return 3*a(n//3)
    elif n%3==1: return 3*a((n - 1)//3) + 2
    else: return 3*a((n + 1)//3) + 1
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 06 2017

Formula

a(1) = 2, a(3n) = 3a(n), a(3n+1) = 3a(n)+2, a(3n-1) = 3a(n)+1.