A327136 Numbers k such that sin(2k) > sin(2k+2) < sin(2k+4).

1, 4, 8, 11, 14, 17, 20, 23, 26, 30, 33, 36, 39, 42, 45, 48, 52, 55, 58, 61, 64, 67, 70, 74, 77, 80, 83, 86, 89, 92, 96, 99, 102, 105, 108, 111, 114, 118, 121, 124, 127, 130, 133, 136, 140, 143, 146, 149, 152, 155, 158, 162, 165, 168, 171, 174, 177, 180, 184

Offset

1,2

Comments

The sequences A026317, A327136, A327137 partition the nonnegative integers.

Conjecture: 1.285 < n*Pi - a(n) < 1.286 for n >= 1.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

(sin 2, sin 4, ...) = (0.9, -0.7, -0.2, 0.9, -0.5, ...) approximately, so that the differences, in sign, are - + + -  + + - - + - - + ..., with "+" in places 2,3,5,6,... (A026317), "- +" starting in places 1,4,8,11,... (A327136), and "- - +" starting in places 7,10,13,16,... (A327137).

Mathematica

z = 500; f[x_] := f[x] = Sin[2 x]; t = Range[1, z];
Select[t, f[#] < f[# + 1] &]    (* A026317 *)
Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A327136 *)
Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]   (* A327137 *)

Crossrefs

Cf. A026309, A246303, A026317.

Sequence in context: A356105 A311030 A311031 * A311032 A311033 A072518

Adjacent sequences: A327133 A327134 A327135 * A327137 A327138 A327139

Keyword

nonn,easy

Author

Clark Kimberling, Aug 23 2019

Status

approved