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Positive integers k satisfying csc(k) > csc(k+1) < csc(k+2).
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%I #10 Sep 01 2014 04:57:40

%S 1,3,5,7,9,11,13,15,17,19,21,24,26,28,30,32,34,36,38,40,42,45,47,49,

%T 51,53,55,57,59,61,63,65,68,70,72,74,76,78,80,82,84,86,89,91,93,95,97,

%U 99,101,103,105,107,109,112,114,116,118,120,122,124,126,128

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

%C A246410, a(n), and A246412 partition the positive integers.

%H Clark Kimberling, <a href="/A246411/b246411.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A158333(n-1) for n<73. - _R. J. Mathar_, Sep 01 2014

%t z = 200; f[x_] := f[x] = Csc[x];

%t Select[Range[1, z], f[#] < f[# + 1] &] (*A246410*)

%t Select[Range[1, z], f[#] > f[# + 1] < f[# + 2] &] (*A246411*)

%t Select[Range[1, 10 z], f[#] > f[# + 1] > f[# + 2] < f[# + 3] &] (*A246412*)

%Y Cf. A246410, A246412.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Aug 25 2014