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A026311 n-th nonnegative integer k satisfying cos(k) > cos(k+1).

%I A026311 #9 Aug 09 2021 18:12:33
%S A026311 0,1,2,6,7,8,13,14,15,19,20,21,25,26,27,31,32,33,34,38,39,40,44,45,46,
%T A026311 50,51,52,57,58,59,63,64,65,69,70,71,75,76,77,78,82,83,84,88,89,90,94,
%U A026311 95,96,101,102,103,107,108,109,113,114,115
%N A026311 n-th nonnegative integer k satisfying cos(k) > cos(k+1).
%C A026311 The sequences A026311, A246300, A246301, A246302 partition the nonnegative integers.
%H A026311 Clark Kimberling, <a href="/A026311/b026311.txt">Table of n, a(n) for n = 1..4000</a>
%t A026311 z = 520; f[x_] := f[x] = Cos[x]; t = Range[0, z];
%t A026311 Select[t, f[#] > f[# + 1] &]  (* A026311 *)
%t A026311 Select[t, f[#] < f[# + 1] > f[# + 2] &]  (* A246300 *)
%t A026311 Select[t, f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (* A246301 *)
%t A026311 Select[t, f[#] < f[# + 1] < f[# + 2] < f[# + 3] > f[# + 4] &] (* A246302 *)
%t A026311 Join[{0},Position[Partition[Cos[Range[120]],2,1],_?(#[[1]]>#[[2]]&),1,Heads -> False]//Flatten] (* _Harvey P. Dale_, Aug 09 2021 *)
%Y A026311 Cf. A246293, A246300, A246301, A246302, A246303 (complement of A026311).
%K A026311 nonn,easy
%O A026311 1,3
%A A026311 _Clark Kimberling_
%E A026311 Comment, Mathematica, Crossrefs by _Clark Kimberling_, Aug 22 2014