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

%I A246389 #7 Jan 18 2024 10:21:21
%S A246389 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 A246389 70,71,76,77,82,83,88,89,90,95,96,101,102,107,108,114,115,120,121,126,
%U A246389 127,132,133,134,139,140,145,146,151,152,158,159,164,165,170,171
%N A246389 Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) >= 0.
%C A246389 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 A246389 Clark Kimberling, <a href="/A246389/b246389.txt">Table of n, a(n) for n = 0..1000</a>
%p A246389 Digits := 100:
%p A246389 isA246389 := proc(k)
%p A246389     if evalf(sin(k)) >= 0 and evalf(sin(k+1)) >= 0 then
%p A246389         return true ;
%p A246389     else
%p A246389         return false ;
%p A246389     end if;
%p A246389 end proc:
%p A246389 A246389 := proc(n)
%p A246389     option remember ;
%p A246389     if n = 1 then
%p A246389         0;
%p A246389     else
%p A246389         for a from procname(n-1)+1 do
%p A246389             if isA246389(a) then
%p A246389                 return a;
%p A246389             end if;
%p A246389         end do:
%p A246389     end if;
%p A246389 end proc:
%p A246389 seq(A246389(n),n=1..100) ; # assumes offset 1 _R. J. Mathar_, Jan 18 2024
%t A246389 z = 400; f[x_] := Sin[x]
%t A246389 Select[Range[0, z], f[#]*f[# + 1] <= 0 &] (* A022844 *)
%t A246389 Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246388 *)
%t A246389 Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &] (* A038130 *)
%t A246389 Select[Range[0, z], f[#]*f[# + 1] > 0 &] (* A054386 *)
%t A246389 Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246389 *)
%t A246389 Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &] (* A246390 *)
%Y A246389 Cf. A022844, A038130, A054386, A246388, A246390.
%K A246389 nonn,easy
%O A246389 0,3
%A A246389 _Clark Kimberling_, Aug 24 2014