A246394 -id:A246394 - cp's OEIS frontend

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

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

Clark Kimberling, Aug 24 2014

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.)

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

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

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 *)

A246395 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) >= 0.

Original entry on oeis.org

0, 5, 6, 11, 12, 13, 18, 19, 24, 25, 30, 31, 37, 38, 43, 44, 49, 50, 55, 56, 57, 62, 63, 68, 69, 74, 75, 81, 82, 87, 88, 93, 94, 99, 100, 101, 106, 107, 112, 113, 118, 119, 125, 126, 131, 132, 137, 138, 143, 144, 145, 150, 151, 156, 157, 162, 163, 169, 170

Offset: 0

Clark Kimberling, Aug 24 2014

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.)

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

Cf. A062389, A246393, A246046, A246394, A246396.

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 *)

A246396 Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) <= 0.

Original entry on oeis.org

2, 3, 8, 9, 15, 16, 21, 22, 27, 28, 33, 34, 35, 40, 41, 46, 47, 52, 53, 59, 60, 65, 66, 71, 72, 77, 78, 79, 84, 85, 90, 91, 96, 97, 103, 104, 109, 110, 115, 116, 121, 122, 123, 128, 129, 134, 135, 140, 141, 147, 148, 153, 154, 159, 160, 165, 166, 167, 172

Offset: 0

Clark Kimberling, Aug 24 2014

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.)

Conjecture: every term t has at least one neighbor which is equal to t plus or minus one. - Harvey P. Dale, Jul 11 2023

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

Cf. A062389, A246393, A246046, A246394, A246395.

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 *)
SequencePosition[Table[If[Cos[k]<=0,1,0],{k,200}],{1,1}][[;;,1]] (* Harvey P. Dale, Jul 11 2023 *)

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

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A246395 Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) >= 0.

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A246396 Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) <= 0.

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