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%I #14 Jun 22 2021 01:06:21
%S 1,4,8,11,14,17,20,23,26,30,33,36,39,42,45,48,52,55,58,61,64,67,70,74,
%T 77,80,83,86,89,92,96,99,102,105,108,111,114,118,121,124,127,130,133,
%U 136,140,143,146,149,152,155,158,162,165,168,171,174,177,180,184
%N Numbers k such that sin(2k) > sin(2k+2) < sin(2k+4).
%C The sequences A026317, A327136, A327137 partition the nonnegative integers.
%C Conjecture: 1.285 < n*Pi - a(n) < 1.286 for n >= 1.
%H Clark Kimberling, <a href="/A327136/b327136.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 1,2
%A _Clark Kimberling_, Aug 23 2019
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