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Numbers k such that cos(k) < cos(k+1) < cos(k+2) > cos(k+3).
4

%I #4 Aug 23 2014 08:50:52

%S 4,11,17,23,29,36,42,48,55,61,67,73,80,86,92,99,105,111,117,124,130,

%T 136,143,149,155,161,168,174,180,186,193,199,205,212,218,224,230,237,

%U 243,249,256,262,268,274,281,287,293,300,306,312,318,325,331,337,344

%N Numbers k such that cos(k) < cos(k+1) < cos(k+2) > cos(k+3).

%C The sequences A026311, A246300, A246301, A246302 partition the nonnegative integers.

%H Clark Kimberling, <a href="/A246301/b246301.txt">Table of n, a(n) for n = 1..1000</a>

%t z = 520; f[x_] := f[x] = Cos[x]; t = Range[0, z];

%t Select[t, f[#] > f[# + 1] &] (* A026311 *)

%t Select[t, f[#] < f[# + 1] > f[# + 2] &] (* A246300 *)

%t Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &] (* A246301 *)

%t Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246302 *)

%Y Cf. A026311, A246300, A246302, A246295.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Aug 22 2014