A327137 - OEIS

%I #14 Jun 22 2021 01:06:30

%S 7,10,13,16,29,32,35,38,51,54,57,60,73,76,79,82,95,98,101,104,117,120,

%T 123,126,139,142,145,148,161,164,167,170,183,186,189,192,205,208,211,

%U 214,227,230,233,236,249,252,255,258,271,274,277,280,293,296,299

%N Numbers k such that sin(2k) > sin(2k+2) > sin(2k+4) < sin(2k+6).

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

%H Clark Kimberling, <a href="/A327137/b327137.txt">Table of n, a(n) for n = 1..10000</a>

%e (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).

%t z = 500; f[x_] := f[x] = Sin[2 x]; t = Range[1, z];

%t Select[t, f[#] < f[# + 1] &]    (* A026317 *)

%t Select[t, f[#] > f[# + 1] < f[# + 2] &]  (* A327136 *)

%t Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &]   (* A327137 *)

%Y Cf. A026309, A246303, A026317.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Aug 23 2019