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Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) >= 0.
4

%I #7 Jan 18 2024 10:21:21

%S 0,1,2,7,8,13,14,19,20,26,27,32,33,38,39,44,45,46,51,52,57,58,63,64,

%T 70,71,76,77,82,83,88,89,90,95,96,101,102,107,108,114,115,120,121,126,

%U 127,132,133,134,139,140,145,146,151,152,158,159,164,165,170,171

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

%C 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.)

%H Clark Kimberling, <a href="/A246389/b246389.txt">Table of n, a(n) for n = 0..1000</a>

%p Digits := 100:

%p isA246389 := proc(k)

%p if evalf(sin(k)) >= 0 and evalf(sin(k+1)) >= 0 then

%p return true ;

%p else

%p return false ;

%p end if;

%p end proc:

%p A246389 := proc(n)

%p option remember ;

%p if n = 1 then

%p 0;

%p else

%p for a from procname(n-1)+1 do

%p if isA246389(a) then

%p return a;

%p end if;

%p end do:

%p end if;

%p end proc:

%p seq(A246389(n),n=1..100) ; # assumes offset 1 _R. J. Mathar_, Jan 18 2024

%t z = 400; f[x_] := Sin[x]

%t Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A022844 *)

%t Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &] (* A246388 *)

%t Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A038130 *)

%t Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A054386 *)

%t Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &] (* A246389 *)

%t Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246390 *)

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

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Aug 24 2014