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%I #16 Dec 07 2019 12:18:26
%S 0,1,-2,3,4,-11,-6,7,-8,9,10,-5,12,13,-38,-33,16,-29,-18,25,-20,21,34,
%T -35,-24,19,-26,27,28,-17,30,37,-32,-15,22,-23,36,31,-14,39,40,-119,
%U -114,43,-92,-99,70,-65,48,97,-110,-87,52,-83,-54,79,-56,75,106,-101
%N Express n in balanced ternary, then reverse the digits, leaving any trailing zeros alone.
%C 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.
%H Indranil Ghosh, <a href="/A160652/b160652.txt">Table of n, a(n) for n = 0..6561</a>
%F a(n) = A134028(n)*3^A007949(n). [_Franklin T. Adams-Watters_, May 24 2009]
%e 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.
%o (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
%o (Python)
%o def a(n):
%o if n==0: return 0
%o r=0
%o dr=1
%o while n%3==0:
%o dr*=3
%o n/=3
%o while n!=0:
%o q=(n + 1)/3
%o r=3*r + dr*(n - 3*q)
%o n=q
%o return r
%o ##print [a(n) for n in range(101)] # _Indranil Ghosh_, Jun 10 2017, after _Franklin T. Adams-Watters_
%Y Cf. A065363, A117962, A117966.
%Y Cf. A057889, A134028, A007949. [_Franklin T. Adams-Watters_, May 24 2009]
%K base,look,sign
%O 0,3
%A _Franklin T. Adams-Watters_, May 21 2009
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