A144609 Sturmian word of slope Pi.

0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1

Offset: 0

Author

N. J. A. Sloane, Jan 13 2009

Keywords

• nonn

Comments

A063438 seems to contain the run lengths of 1's. - R. J. Mathar, May 30 2025

Crossrefs

See A144595 for further details.

Seems to be very similar to A070127. Is this a coincidence?

Cf. A063438, A076539 (partial sums).

Programs

Maple

Digits := 500 :
x :=1 ;
y :=0 ;
slop := Pi ;
printf("0,") ;
for n from 1 to 300 do
    if evalf((y+1)/x-slop) > 0 then
        x := x+1 ;
        printf("0,") ;
    else
        y := y+1 ;
        printf("1,") ;
    end if;
end do: # R. J. Mathar, May 30 2025

Mathematica

christoffel[s_, M_] := Module[{n, x = 1, y = 0, ans = {0}}, Do[ If[y + 1 <= s*x, AppendTo[ans, 1]; y++, AppendTo[ans, 0]; x++], {n, 1, M}]; ans]; christoffel[Pi, 105] (* Robert G. Wilson v, Feb 02 2017, after Jean-François Alcover, Sep 19 2016, A274170 *)