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A246413 Positive integers k satisfying csc(k) > csc(k+1).

%I A246413 #8 Jul 27 2020 20:06:33
%S A246413 1,3,5,7,9,11,13,15,17,19,21,24,26,28,30,32,34,36,38,40,42,44,45,47,
%T A246413 49,51,53,55,57,59,61,63,65,68,70,72,74,76,78,80,82,84,86,88,89,91,93,
%U A246413 95,97,99,101,103,105,107,109,112,114,116,118,120,122,124,126
%N A246413 Positive integers k satisfying csc(k) > csc(k+1).
%C A246413 a(n), A246414, and A246415 partition the positive integers.
%H A246413 Clark Kimberling, <a href="/A246413/b246413.txt">Table of n, a(n) for n = 1..1000</a>
%t A246413 z = 200;
%t A246413 f[x_] := f[x] = Csc[x];
%t A246413 Select[Range[1, z], f[#] > f[# + 1] &]  (*A246413*)
%t A246413 Select[Range[1, z], f[#] < f[# + 1] > f[# + 2] &]  (*A246414 *)
%t A246413 Select[Range[1, z], f[#] < f[# + 1] < f[# + 2] > f[# + 3] &]  (*A246415*)
%t A246413 Position[Partition[Csc[Range[130]],2,1],_?(#[[1]]>#[[2]]&),1,Heads-> False]// Flatten (* _Harvey P. Dale_, Jul 27 2020 *)
%Y A246413 Cf. A246414, A246415, A246410 (complement of a(n)).
%K A246413 nonn,easy
%O A246413 1,2
%A A246413 _Clark Kimberling_, Aug 25 2014