A216430 (-1)^A081603(n), parity of the number of 2's in the ternary expansion of n.

1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1

Offset

1

Links

Table of n, a(n) for n=1..90.

A. Aksenov, The Newman phenomenon and Lucas sequence, arXiv:1108.5352, chapter 6.

Example

a(7) = -1 because 7 is 21 (has one 2s) in base 3, and (-1)^1 = -1.
a(8) = 1 because 8 is 22 (has two 2s) in base 3, and (-1)^2 = 1.

Maple

A081603 := proc(n)
    local a, d ;
    a := 0 ;
    for d in convert(n, base, 3) do
        if d = 2 then
            a := a+1 ;
        end if;
    end do;
    a;
end proc:
A216430 := proc(n)
    (-1)^A081603(n) ;
end proc:
seq(A216430(n), n=1..90) ;

Mathematica

Table[(-1)^DigitCount[n, 3, 2], {n, 90}] (* Alonso del Arte, Sep 08 2012 *)

Crossrefs

Sequence in context: A209661 A033999 A000012 * A232544 A309873 A162511

Adjacent sequences: A216427 A216428 A216429 * A216431 A216432 A216433

Keyword

sign,easy,base

Author

R. J. Mathar, Sep 08 2012

Status

approved