

A346524


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


0



0, 1, 1, 3, 4, 0, 3, 4, 2, 9, 10, 2, 12, 13, 3, 2, 3, 1, 9, 10, 4, 12, 13, 5, 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, 12, 4, 3, 4, 2, 27, 28, 10, 30, 31, 11, 6, 7, 5, 36, 37
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OFFSET

0,4


COMMENTS

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.
Those n which do not contain a 2 in ternary (A005836) remain unchanged and are record highs.
Those n which in ternary are a binary number prefixed by a 2 (A319953) give the record lows.


LINKS



EXAMPLE

For n = 208893 = 101121112210_3, changing each 2 to a 1 gives 101111111110; interpreting each "" as a subtraction operator gives 1011_3  1111_3  1_3  110_3 = 31  40  1  12 = 22, so a(208893) = 22.
For n = 25 = 221_3, changing the 2's to (1)'s gives 111; 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.


PROG

(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=i1)); ret + fromdigits(v[1..lo], 3); \\ Kevin Ryde, Jul 23 2021


CROSSREFS



KEYWORD

base,sign


AUTHOR



STATUS

approved



