A246389 Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) >= 0.

0, 1, 2, 7, 8, 13, 14, 19, 20, 26, 27, 32, 33, 38, 39, 44, 45, 46, 51, 52, 57, 58, 63, 64, 70, 71, 76, 77, 82, 83, 88, 89, 90, 95, 96, 101, 102, 107, 108, 114, 115, 120, 121, 126, 127, 132, 133, 134, 139, 140, 145, 146, 151, 152, 158, 159, 164, 165, 170, 171

Offset: 0

Author

Clark Kimberling, Aug 24 2014

Keywords

• nonn
• easy

Comments

A246388 and A038130 (Beatty sequence for 2*Pi) partition A022844 (Beatty sequence for Pi). Likewise, A054386, the complement of A022844, is partitioned by A246389 and A246390. (See the Mathematica program.)

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A022844, A038130, A054386, A246388, A246390.

Programs

Maple

Digits := 100:
isA246389 := proc(k)
    if evalf(sin(k)) >= 0 and evalf(sin(k+1)) >= 0 then
        return true ;
    else
        return false ;
    end if;
end proc:
A246389 := proc(n)
    option remember ;
    if n = 1 then
        0;
    else
        for a from procname(n-1)+1 do
            if isA246389(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A246389(n),n=1..100) ; # assumes offset 1 R. J. Mathar, Jan 18 2024

Mathematica

z = 400; f[x_] := Sin[x]
Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A022844 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246388 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A038130 *)
Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A054386 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246389 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246390 *)