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

1,1

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

Formula

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A233770 A138283 A308682 * A217568 A320871 A154200

Adjacent sequences: A117965 A117966 A117967 * A117969 A117970 A117971

Keyword

base,nonn

Author

Franklin T. Adams-Watters, Apr 05 2006

Status

approved