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A346524 Write n in ternary, replace each 2 with -1, interpret each "-" as a subtraction operator, and evaluate the resulting expression in ternary.

%I A346524 #54 Aug 01 2021 14:44:33
%S A346524 0,1,-1,3,4,0,-3,-4,-2,9,10,2,12,13,3,-2,-3,-1,-9,-10,-4,-12,-13,-5,
%T A346524 -4,-5,-3,27,28,8,30,31,9,0,-1,1,36,37,11,39,40,12,1,0,2,-8,-9,-3,-11,
%U A346524 -12,-4,-3,-4,-2,-27,-28,-10,-30,-31,-11,-6,-7,-5,-36,-37
%N A346524 Write n in ternary, replace each 2 with -1, interpret each "-" as a subtraction operator, and evaluate the resulting expression in ternary.
%C A346524 Instead of interpreting the -1 as done in balanced ternary (as in A117966), read the newly formed string as a mathematical expression and evaluate it in ternary as if each "-" is a subtraction operator.
%C A346524 Those n which do not contain a 2 in ternary (A005836) remain unchanged and are record highs.
%C A346524 Those n which in ternary are a binary number prefixed by a 2 (A319953) give the record lows.
%e A346524 For n = 208893 = 101121112210_3, changing each 2 to a -1 gives 1011-1111-1-110; interpreting each "-" as a subtraction operator gives 1011_3 - 1111_3 - 1_3 - 110_3 = 31 - 40 - 1 - 12 = -22, so a(208893) = -22.
%e A346524 For n = 25 = 221_3, changing the 2's to (-1)'s gives -1-11; interpreting the leading "-" as a unary minus (so the expression starts with a negative 1) and the remaining "-" as a subtraction operator gives -1_3 - 11_3 = -1 - 4 = -5, so a(25) = -5.
%o A346524 (PARI) a(n) = my(v=digits(n,3),lo=#v,ret=0); forstep(i=#v,1,-1, if(v[i]==2, v[i]=1; ret -= fromdigits(v[i..lo],3); lo=i-1)); ret + fromdigits(v[1..lo],3); \\ _Kevin Ryde_, Jul 23 2021
%Y A346524 Cf. A005836 (fixed points), A319953.
%Y A346524 Cf. A117966.
%K A346524 base,sign
%O A346524 0,4
%A A346524 _Johnathan Abdoo_, Jul 21 2021