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

%I #8 Apr 01 2024 10:20:32

%S 1,7,14,20,26,33,39,45,51,58,64,70,77,83,89,95,102,108,114,121,127,

%T 133,139,146,152,158,165,171,177,183,190,196,202,208,215,221,227,234,

%U 240,246,252,259,265,271,278,284,290,296,303,309,315,322,328,334,340

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

%C The sequences A246303, A246304, A246305, A246306 partition the nonnegative integers.

%H Clark Kimberling, <a href="/A246305/b246305.txt">Table of n, a(n) for n = 1..1000</a>

%t z = 500; f[x_] := f[x] = Cos[x]; t = Range[0, z];

%t Select[t, f[#] < f[# + 1] &] (* A246303 *)

%t Select[t, f[#] > f[# + 1] < f[# + 2] &] (* A246304 *)

%t Select[t, f[#] > f[# + 1] > f[# + 2] < f[# + 3] &] (* A246305 *)

%t Select[t, f[#] > f[# + 1] > f[# + 2] > f[# + 3] < f[# + 4] &] (* A246306 *)

%Y Cf. A026303, A246304, A246306, A026311 (complement of A246303).

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Aug 22 2014

%E Definition corrected by _Georg Fischer_, Apr 01 2024