A160652 Express n in balanced ternary, then reverse the digits, leaving any trailing zeros alone.

0, 1, -2, 3, 4, -11, -6, 7, -8, 9, 10, -5, 12, 13, -38, -33, 16, -29, -18, 25, -20, 21, 34, -35, -24, 19, -26, 27, 28, -17, 30, 37, -32, -15, 22, -23, 36, 31, -14, 39, 40, -119, -114, 43, -92, -99, 70, -65, 48, 97, -110, -87, 52, -83, -54, 79, -56, 75, 106, -101

Offset: 0

Author

Franklin T. Adams-Watters, May 21 2009

Keywords

• base
• look
• sign

Comments

This sequence, together with its negative extension a(-n) = -a(n) is a self-inverse permutation of the integers. The absolute values are a self-inverse permutation of the nonnegative integers.

Examples

			87 in balanced ternary is 101(-1)0; leaving the final 0 and reversing the remaining digits gives (-1)1010, which is -51; so a(87) = -51.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..6561

Crossrefs

Cf. A065363, A117962, A117966.

Cf. A057889, A134028, A007949. [Franklin T. Adams-Watters, May 24 2009]

Programs

PARI

a(n)=local(r,dr,q);if(n==0,0,r=0;dr=1;while(n%3==0,dr*=3;n\=3);while(n!=0,q=(n+1)\3;r=3*r+dr*(n-3*q);n=q);r) \\ Franklin T. Adams-Watters, May 24 2009

Python

def a(n):
    if n==0: return 0
    r=0
    dr=1
    while n%3==0:
        dr*=3
        n/=3
    while n!=0:
        q=(n + 1)/3
        r=3*r + dr*(n - 3*q)
        n=q
    return r
##print [a(n) for n in range(101)] # Indranil Ghosh, Jun 10 2017, after Franklin T. Adams-Watters

Formula

a(n) = A134028(n)*3^A007949(n). [Franklin T. Adams-Watters, May 24 2009]