cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A038130 Beatty sequence for 2*Pi.

Original entry on oeis.org

0, 6, 12, 18, 25, 31, 37, 43, 50, 56, 62, 69, 75, 81, 87, 94, 100, 106, 113, 119, 125, 131, 138, 144, 150, 157, 163, 169, 175, 182, 188, 194, 201, 207, 213, 219, 226, 232, 238, 245, 251, 257, 263, 270, 276, 282, 289, 295, 301, 307, 314, 320, 326, 333, 339, 345
Offset: 0

Views

Author

Felice Russo

Keywords

Comments

a(n) = floor[circumference of a circle of radius n]. - Mohammad K. Azarian, Feb 29 2008
This sequence consists of the nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) >= 0; thus this sequence and A246388 partition A022844 (the Beatty sequence for Pi). - Clark Kimberling, Aug 24 2014

Links

Crossrefs

Complement of A108586.
For ceiling (2*Pi*n) see A004082.
Cf. A022844, A140758, A108592, A246388.

Programs

  • Mathematica
    Table[Floor[2 n*Pi], {n, 0, 100}] (* or *)
Select[Range[0, 628], Sin[#] <= 0 && Sin[# + 1] >= 0 &] (* Clark Kimberling, Aug 24 2014 *)

Formula

a(n) = floor(2*Pi*n).
a(n) = A004082(n+1) - 1. - John W. Nicholson, Mar 20 2025

Extensions

More terms from Mohammad K. Azarian, Feb 29 2008

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Aug 24 2014

Keywords

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

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 *)

A246393 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) <= 0.

Original entry on oeis.org

1, 7, 14, 20, 26, 32, 39, 45, 51, 58, 64, 70, 76, 83, 89, 95, 102, 108, 114, 120, 127, 133, 139, 146, 152, 158, 164, 171, 177, 183, 190, 196, 202, 208, 215, 221, 227, 234, 240, 246, 252, 259, 265, 271, 278, 284, 290, 296, 303, 309, 315, 322, 328, 334, 340
Offset: 0

Views

Author

Clark Kimberling, Aug 24 2014

Keywords

Comments

A246393 and A246394 partition A062389 (the nonhomogeneous Beatty sequence {floor((n-1/2)*Pi)}). Likewise, A246046, the complement of A062389, is partitioned by A246395 and A246396. (See the Mathematica program.)

Links

Crossrefs

Cf. A062389, A246394, A246046, A246395, A246396, A246388.

Programs

  • Mathematica
    z = 400; f[x_] := Cos[x]
Select[Range[0, z], f[#]*f[# + 1] <= 0 &]  (* A062389 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] <= 0 &]  (* A246393 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] >= 0 &]  (* A246394 *)
Select[Range[0, z], f[#]*f[# + 1] > 0 &]  (* A246046 *)
Select[Range[0, z], f[#] >= 0 && f[# + 1] >= 0 &]  (* A246395 *)
Select[Range[0, z], f[#] <= 0 && f[# + 1] <= 0 &]  (* A246396 *)

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

Views

Author

Clark Kimberling, Aug 24 2014

Keywords

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

Crossrefs

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

Programs

  • 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 *)
SequencePosition[Table[If[Sin[n]<=0,1,0],{n,200}],{1,1}][[;;,1]] (* Harvey P. Dale, Apr 02 2023 *)
Showing 1-4 of 4 results.

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