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

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

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

Table of n, a(n) for n=0..64.

Example

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.
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.

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

Crossrefs

Cf. A005836 (fixed points), A319953.

Cf. A117966.

Sequence in context: A200514 A063405 A360533 * A139401 A110061 A363804

Adjacent sequences: A346521 A346522 A346523 * A346525 A346526 A346527

Keyword

base,sign

Author

Johnathan Abdoo, Jul 21 2021

Status

approved