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A246414 Positive integers k satisfying csc(k) < csc(k+1) > csc(k+2).

%I A246414 #8 May 05 2023 15:04:26
%S A246414 2,4,6,8,10,12,14,16,18,20,23,25,27,29,31,33,35,37,39,41,43,46,48,50,
%T A246414 52,54,56,58,60,62,64,67,69,71,73,75,77,79,81,83,85,87,90,92,94,96,98,
%U A246414 100,102,104,106,108,111,113,115,117,119,121,123,125,127,129
%N A246414 Positive integers k satisfying csc(k) < csc(k+1) > csc(k+2).
%C A246414 A246413, a(n), and A246415 partition the positive integers.
%H A246414 Clark Kimberling, <a href="/A246414/b246414.txt">Table of n, a(n) for n = 1..1000</a>
%t A246414 z = 200;
%t A246414 f[x_] := f[x] = Csc[x];
%t A246414 Select[Range[1, z], f[#] > f[# + 1] &]  (*A246413*)
%t A246414 Select[Range[1, z], f[#] < f[# + 1] > f[# + 2] &]  (*A246414 *)
%t A246414 Select[Range[1, z], f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (*A246415*)
%t A246414 Position[Partition[Csc[Range[200]],3,1],_?(#[[1]]<#[[2]]>#[[3]]&),1,Heads->False]//Flatten (* _Harvey P. Dale_, May 05 2023 *)
%Y A246414 Cf. A246413, A246415.
%K A246414 nonn,easy
%O A246414 1,1
%A A246414 _Clark Kimberling_, Aug 25 2014