A246389 -id:A246389 - cp's OEIS frontend

A246388 Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) <= 0.

3, 9, 15, 21, 28, 34, 40, 47, 53, 59, 65, 72, 78, 84, 91, 97, 103, 109, 116, 122, 128, 135, 141, 147, 153, 160, 166, 172, 179, 185, 191, 197, 204, 210, 216, 223, 229, 235, 241, 248, 254, 260, 267, 273, 279, 285, 292, 298, 304, 311, 317, 323, 329, 336, 342

Offset: 0

Clark Kimberling, Aug 24 2014

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.)

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

Cf. A022844, A038130, A054386, A246389, A246390.

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 *)

A246390 Nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) <= 0.

Original entry on oeis.org

4, 5, 10, 11, 16, 17, 22, 23, 24, 29, 30, 35, 36, 41, 42, 48, 49, 54, 55, 60, 61, 66, 67, 68, 73, 74, 79, 80, 85, 86, 92, 93, 98, 99, 104, 105, 110, 111, 112, 117, 118, 123, 124, 129, 130, 136, 137, 142, 143, 148, 149, 154, 155, 156, 161, 162, 167, 168, 173

Offset: 0

Clark Kimberling, Aug 24 2014

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.)

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

Cf. A022844, A038130, A054386, A246388, A246389.

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 *)
SequencePosition[Table[If[Sin[n]<=0,1,0],{n,200}],{1,1}][[;;,1]] (* Harvey P. Dale, Apr 02 2023 *)

A369273 Nonnegative numbers k satisfying sin(k) < sin(k+1) < sin(k+2).

Original entry on oeis.org

0, 5, 6, 11, 12, 17, 18, 24, 25, 30, 31, 36, 37, 42, 43, 44, 49, 50, 55, 56, 61, 62, 68, 69, 74, 75, 80, 81, 86, 87, 88, 93, 94, 99, 100, 105, 106, 112, 113, 118, 119, 124, 125, 130, 131, 132, 137, 138, 143, 144, 149, 150, 156, 157, 162, 163, 168, 169, 174, 175, 181, 182, 187, 188, 193, 194

Offset: 1

R. J. Mathar, Jan 18 2024

Subsequence of terms in A026309: The smaller of two consecutive terms there.

The terms A246389(.)-2 almost match the terms here; the exceptions are terms 178, 220, 266, 310, 555, 599, ... in A246389 where the associates 176, 218, 264, 308, ... are not in this sequence. - Hugo Pfoertner, Jan 18 2024

Cf. A026309, A369274, A369275.

isA369273 := proc(k)
    local s ;
    s := [seq(evalf(sin(k+i)),i=0..2)] ;
    if s[1] < s[2] and s[2] < s[3] then
        true;
    else
        false;
    end if;
end proc:
A369273 := proc(n)
    option remember ;
    if n = 1 then
        0;
    else
        for a from procname(n-1)+1 do
            if isA369273(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
seq(A369273(n),n=1..100) ;

Select[Range[0,194], Sin[#]James C. McMahon, Jan 22 2024 *)

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A246388 Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) <= 0.

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A246390 Nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) <= 0.

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A369273 Nonnegative numbers k satisfying sin(k) < sin(k+1) < sin(k+2).

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