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%I #14 Jun 22 2021 01:06:56
%S 1,4,7,10,13,16,19,23,26,29,32,35,38,41,45,48,51,54,57,60,63,67,70,73,
%T 76,79,82,85,89,92,95,98,101,104,107,111,114,117,120,123,126,129,133,
%U 136,139,142,145,148,151,155,158,161,164,167,170,173,176,180,183
%N Numbers k such that cos(2k) > cos(2k+2) < cos(2k+4).
%C The sequences A327138, A327139, A327140 partition the positive integers.
%H Clark Kimberling, <a href="/A327139/b327139.txt">Table of n, a(n) for n = 1..10000</a>
%F (cos 2, cos 4, ...) = (-0.4, -0.6, 0.9, -0.1, -0.8, ...) approximately, so that the differences, in sign, are - + - - + - - + - - + +, with "+" in places 2,5,8,11,12,... (A327138), "- +" starting in places 1,4,7,10,13,... (A327139), and "- - +" starting in places 3,6,9,22,25,... (A327140).
%t z = 500; f[x_] := f[x] = Cos[2 x]; t = Range[1, z];
%t Select[t, f[#] < f[# + 1] &] (* A327138 *)
%t Select[t, f[#] > f[# + 1] < f[# + 2] &] (* A327139 *)
%t Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &] (* A327140 *)
%Y Cf. A026309, A246303, A026317, A327138.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Aug 23 2019
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